Exploitation of pilot signals for blind resilient detection and geo-observable estimation of navigation signals

ABSTRACT

A method and apparatus detects and estimates geo-observables of navigation signals employing civil formats with repeating baseband signal components, i.e., “pilot signals,” including true GNSS signals generated by satellite vehicles (SV&#39;s) or ground beacons (pseudolites), and malicious GNSS signals, e.g., spoofers and repeaters. Multi-subband symbol-rate synchronous channelization can exploit the full substantive bandwidth of the GNSS signals with managed complexity in each subband. Spatial/polarization receivers can be provided to remove interference and geolocate non-GNSS jamming sources, as well as targeted GNSS spoofers that emulate GNSS signals. This can provide time-to-first-fix (TTFF) over much smaller time intervals than existing GNSS methods; can operate in the presence of signals with much wider disparity in received power than existing techniques; and can operate in the presence of arbitrary multipath.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a Continuation of U.S. patent application Ser. No.16/701,144, filed on Dec. 2, 2019, now U.S. Pat. No. 11,125,888, whichclaims priority to Provisional Appl. No. 62/773,589, filed Nov. 30,2018; and Provisional Appl. No. 62/773,605, filed Nov. 30, 2018; andU.S. patent application Ser. No. 16/701,144 is a Continuation-in-Part ofU.S. patent application Ser. No. 15/731,417, filed Jun. 5, 2017, nowU.S. Pat. No. 10,775,510, which claims priority to Provisional Appl. No.62/392,623, filed Jun. 6, 2016 and Provisional Appl. No. 62/429,029,filed Dec. 1, 2016; all of which are hereby incorporated by reference intheir entireties and all of which this application claims priority underat least 35 U.S.C. 120 and/or any other applicable provision in Title 35of the United States Code.

FIELD OF THE INVENTION

Aspects of the disclosure relate generally to location determination,and more particularly to detecting or determining geo-observables ofnavigation signals transmitted by satellite vehicles (SV's) in GlobalNavigation Satellite Systems (GNSS), airborne non-SV beacons (e.g.,pseudolites), and ground-based beacons.

BACKGROUND

The American Global Positioning System (GPS) L1 coarse acquisitionsignal (commonly referred to as the “L1 C/A signal,” or more recently asthe “L1 legacy signal”), originally developed as a means for aidingacquisition of the military-grade P (later encrypted P(Y)) code, hasgained near-ubiquitous use as a means for navigation and carrier/timingsynchronization in civil positioning, navigation, and timing (PNT)systems. This is due in part to the GPS network's worldwide visibility;the publically disclosed and well-known structure of the L1 C/Asignal-in-space (SiS); and the ready availability of mature, low-costhardware for receiving the L1 C/A signal.

The success of the GPS L1 C/A signal has resulted in incorporation of“civil” modes in all of the Global Navigation Satellite System (GNSS)signals developed to date, e.g., the GLONASS, Galileo, Beidou, andNAVIC/IRNSS signals. In addition, the need for additional precision tosupport civil PNT operation in urban canyons and autonomous navigationsystems has spurred the development of the wideband civil GPS L5,Galileo E5B, and E6B/C modes, and the Japanese Quasi-Zenith SatelliteSystem (QZSS), which is transmits a version of the civil GPS L5 signalfrom geosynchronous orbit. Moreover, similar civil signal modes havebeen proposed as GNSS-like ground and air beacons, such as the Locata'sLocataLite signal, which emulates the GPS C/A signal with a ×10spreading rate in the 2.4-2.485 GHz ISM band. All of these civil modespossess a common modulation format, referred to herein asmodulation-on-symbol direct-sequence spread spectrum (MOS-DSSS), inwhich a baseband symbol stream, typically (but not always) operating ata 1,000 sample-per-second (1 ksps) symbol rate, is modulated by ahigher-rate ranging code that repeats every symbol.

Since its inception, the only method used to acquire, demodulate, anddetermine geo-observables of these navigation signals in PNTapplications has been matched-filter despreading methods. These methodsoperate by correlating the ranging code (or a set of ranging codes thatthe transmitter may be using) against the received signal and adjustingthe carrier and timing offset of that code (referred to herein asgeo-observables of the received navigation signal) until it aligns withthe code received from the GNSS transmitter. However, matched filterdespreading possesses inherent limitations that can degrade itsperformance in many reception environments. Known limitations includethe following:

-   -   Slow cold-start time-to-first-fix (TTFF), even in the most        benign environments. In a cold start scenario, the receiver does        not know the specific ranging codes used by any of the GNSS        satellite vehicles, nor does it know the timing phase or        frequency offset of those codes, hence it must search over code,        timing, and frequency to synchronize with a single satellite.        Cold-start TTFF can be on the order of minutes, and in addition        can be quite power consumptive.    -   High sensitivity to multipath interference, including        inadvertent multipath induced by the specular reflectors in the        vicinity of the receiver, which can distort the ranging codes        and degrade or destroy correlation peaks, and synthetic        multipath induced by malicious repeaters. Inadvertent multipath        is especially acute in urban and indoor navigation and        localization scenarios.    -   High susceptibility to strong co-channel interference, including        near-far interference from local beacons, malicious non-targeted        spoofing signals, and malicious jamming signals. The GNSS        signals deployed to date only provide a despreading gain of        30-40 dB, based on the chip-rate of the GNSS ranging codes, most        of which is needed to raise the GNSS signal above the background        noise; hence the signal is easily jammed by many types of        interference. An additional 10-13 dB gain can be obtained by        exploiting additional structure of the baseband symbol stream.        However, this further increases TTFF in cold-start acquisition        scenarios.    -   High susceptibility to targeted or “aligned” covert spoofers        that can use knowledge of the ranging code from the satellite        and rough location of the receiver platform to duplicate and        attempt to supplant signals from those satellites.    -   Reliance on ancillary anti-spoofing (AS) codes, e.g., the GPS L1        P(Y) code, to overcome jamming and spoofing events. This        reliance increases the cost of the receiver, limits AS        capability to a subset of military receivers (again, with        inherently higher cost), and introduces a host of physical        security measures and restrictions to prevent compromise of        AS-capable receivers.    -   Need to maintain a library of all of the GNSS ranging codes, or        seeds used to initiate the codes, in order to implement the        despreader. This can complicate the receiver architecture,        especially for “multi-GNSS receivers” that are designed to        exploit civil signals generated by multiple families of        satellites.        Moreover, there is a perceived (but not real) need for        matched-filter despreaders to receive and sample signals over        wide bandwidths, constrained to a large integer multiple of the        ranging code chip-rate, e.g., 1.023 million chips per second        (Mcps) for the GPS C/A code, and 10.23 Mcps for the GPS L5 short        code, in order to fully exploit the processing gain of the code,        overcome aforementioned channel multipath effects, and (in        military GPS receivers) exploit moderate and long codes overlaid        on top of the short civil code. This perceived need is further        complicated in multi-GNSS radios, which must accommodate wide        ranges of chip rates and bandwidths.

SUMMARY

The following summarizes some aspects of the present disclosure toprovide a basic understanding of the discussed technology. This summaryis not an extensive overview of all contemplated features of thedisclosure, and is intended neither to identify key or critical elementsof all aspects of the disclosure nor to delineate the scope of any orall aspects of the disclosure. Its sole purpose is to present someconcepts of one or more aspects of the disclosure in summary form as aprelude to the more detailed description that follows.

Disclosed aspects provide for detecting and obtaining geo-observables ofnavigation signals generated by satellite vehicles (SV's) in GlobalNavigation Satellite Systems (GNSS), and generated by ground-based orairborne non-SV beacons, e.g., pseudolites. This includes effectingdetection and geo-observable estimation in environments populated withmany sources, including malicious sources intending to disrupt orsubvert information provided by legitimate sources, for example,non-GNSS jammers, spoofers that emulate GNSS signals, and repeaters thatcan record and replay environments containing true GNSS signals.Furthermore, this includes effecting said detection and geo-observableestimation in environments subject to potentially severe differences inpower levels between such signals, for example, “near-far interference”between remote GNSS signals and nearby ground or air based beacons,jammers, and spoofers.

Aspects of the disclosure can achieve these and other goals byexploiting the massive spectral redundancy of navigation signalsemploying modulation-on-symbol direct-sequence spread spectrum(MOS-DSSS) modulation formats, in which a baseband symbol sequence isspread by a ranging code that repeats every each baseband symbol. Noveland powerful methods for exploiting this signal structure areintroduced. For example, aspects described herein can exploit the time,frequency and code diversity of those signals, to implement adaptivelinear combining methods and linear-algebraic combiner adaptationalgorithms to detect all of the MOS-DSSS navigation signals in thereceived environment at the maximum signal-to-interference-and-noiseratio (max-SINR) achievable by the combiners; estimate keygeo-observables of those detected signals; identify detected malicioussources ahead of or during PNT acquisition and tracking operations;prevent those malicious sources from corrupting or subverting the PNToperation; and optionally alert the receiver to the presence of thosesources, and/or geolocate those malicious sources. In aspects employingmultifeed receivers wherein multiple spatial and/or polarization diverseantennas are coupled to multiple receivers that are receptive to theMOS-DSSS navigation signals, aspects of the disclosure can additionallyexploit the additional spatial and/or polarization diversity ofnavigation and non-navigation (e.g., jamming) signals to further removenon-navigation signals from the received MOS-DSSS navigation signals,and to remove targeted spoofing signals that closely emulate the time,frequency, and code diversity of navigation signals the spoofers areintending to displace at a victim receiver.

Moreover, such aspects can perform all of these operations withoutknowledge of, a search over, or synchronization to the specific rangingcodes employed by each navigation signal. As a consequence, the systemdescribed herein can enable faster time-to-first-fix (TTFF) thanconventional navigation receivers that require a search over rangingcode parameters, and additional robustness to multipath interference(including synthetic multipath induced by repeaters) that can impairthat search. Disclosed aspects also provide enhanced compatibility withimplementations employing software-defined radio (SDR) architectures,including general-purpose SDR (GPSDR) architectures that are notoptimized to GNSS applications, further improving cost and flexibilityof the system.

Aspects disclosed herein can adapt symbol-rate (e.g., not chip-rate)synchronous reception and channelization structure, using bothpurpose-built equipment designed specifically for GNSS bands and signalsof interest, or general-purpose software-defined receiver (GPSDR)equipment, e.g., Ettus Research Universal Research Software Peripheral(USRP) radios such as the B200mini-series device, which can employ amuch wider range of sampling rates and bandwidths, and which employanalog-to-digital converters (ADC) with 8 or more bits per in-phase (I)and quadrature (Q) rail, allowing implementation of sophisticated jammermitigation techniques and operation in severe multipath environments.This is in contrast to GNSS-specific SDR (GNSS-SDR) equipment, e.g., theMaxim MAX2769 series of Universal GNSS Receivers, which are employ ADC'swith sampling rates preset to integer multiple of the GNSS chip-rate,e.g., 16.238 Msps (16×1.023 Msps), and with ADC precisions of 1-2 bitsper I and Q rail, or 3 bits per I rail, thereby substantively worseningthe receivers' vulnerability to jamming measures and severe multipath.

Aspects disclosed herein can be configured to operate in devices,systems, and methods disclosed in nonprovisional patent application Ser.No. 15/731,417, “Blind Despreading of Civil GNSS Signals for ResilientPNT Applications” (the '417 NPA), incorporated herein by reference. Suchaspects can be employed in a method, system, and/or apparatus forreceiving, blindly despreading, and determining geo-observables, of truecivil Global Navigation Satellite Systems (GNSS) navigation signalsgenerated by any of the set of satellite vehicles and ground beacons,amongst false echoes and malicious GNSS signals from spoofers andrepeaters; for identifying malicious GNSS signals, and preventing thosesignals from corrupting or capturing PNT tracking operations; and forgeolocating malicious GNSS signals. Some aspects can be configured forspatial/polarization diverse receivers that remove non-GNSS jammersreceived by the system, as well as targeted GNSS spoofers that canotherwise emulate GNSS signals received at victim receivers.

Aspects of the disclosure are further described for exploitingnavigation signal modulation formats in which a component of thebaseband symbol sequence, referred to herein as a “pilot signal,” isperiodically repeated. Novel and powerful methods for exploiting thissignal structure is an additional focus of aspects disclosed herein. Forexample, means are described for exploiting the period or content ofthose pilot signals to effect “partially blind” signal detection andgeo-observable estimation methods that are highly efficient relative toequivalent “fully blind” methods that exploit more general properties ofthe baseband symbol sequence; and that can perform this detection andgeo-observable estimation at much lower received incident powers (RIP's)than equivalent fully-blind methods.

Aspects of the disclosure are further described for exploitingnavigation or symbol streams provided by third parties. It is known thatfully-blind despreading methods introduce complexity inherent to thegoals and needs of the method; specifically, the demodulation (symbolestimation) step. This step inherently requires a despreader outputsignal-to-noise ratio (SNR) that is high enough to determine thebaseband symbols after integration over each symbol, or to demodulatethe navigation sequence after integration over each navigation symbol.This introduces a fundamental “acquisition threshold” for any fullyblind method, i.e., the received incident power (RIP) or despreadsignal-to-inference-and-noise ratio (SINR) at which navigation signalscan be reliably demodulated by the methods, or for that matter for anyconventional matched-filter despreading method. This also places a limiton the accuracy of any geo-observable estimation algorithm that relieson that demodulated navigation data, which will be degraded by errors inthat data.

However, in many use scenarios, baseband symbol or navigation sequencescan be obtained from third-party sources. For example, in some usescenarios, PNT-capable platforms may possess GNSS reception devices thatcan receive, despread, and demodulate navigation data on their own innon-challenged environments. For example, recent versions of Androidprovide raw GPS navigation bit-streams along with GNSS measurementresults. In other use scenarios, a PNT-capable or noncapable platformmay possess communication links to other PNT-capable platforms ornetwork infrastructure capable of receiving, despreading, anddemodulating navigation signals. For example CORS(Continuously-Operating Reference Stations) decode navigation data andmake it available in a decoded format that can be obtained over theInternet.

This third-party data can be used to implement “partially-blind” methodsthat can achieve the blind signal separation, jammer/spoofer resilience,near-far interference resilience, and multipath robustness without theneed for, or sensitivity to, demodulating the received navigation data.Among other advantages, these approaches can develop resilient PNT(RPNT) analytics over integration times that are substantively (intheory, arbitrarily) longer than a single baseband or navigation symbol,allowing accurate signal geo-observable estimation well below theacquisition threshold required for both any fully-blind despreadingmethod. In many use scenarios, this performance can furthermore beprovided at substantively lower complexity than fully-blind methods thatrequire demodulation of the navigation sequence.

Aspects disclosed herein also allow the use of multi-subbandarchitectures in which symbol-rate synchronous channelizers are employedover multiple subbands within the GNSS signal band, or symbol-ratesynchronous channelizer bins covering the GNSS signal bandwidth areorganized into subbands within the GNSS signal band. In these aspects,linear combiners, and interference-excising linear-algebraic combineradaptation algorithms, are employed to develop detection features andsignal estimates within each subband metrics, which are then combinedacross subbands. The resultant method can exploit the full bandwidth ofthe GNSS signal, with a system complexity that scales linearly with thebandwidth exploited (number of subbands), and can constrain thedimensionality (and therefore complexity) of linear combiner adaptationoperations employed in each subband to just that needed to effectivelyexcise interference encountered within that subband. The multi-subbandapproach also provides a means for naturally excising non-tonalnarrowband jamming signals, by selectively and adaptively suppressingsubbands containing strong non-GNSS interference.

In one aspect, a low-cost single-feed reception system and multi-subbandsymbol-rate synchronous channelizer is presented that can developresilient positioning, navigation, and timing (RPNT) analytics for civilmodes of Global Navigation Satellite System (GNSS) signals generated bysatellite vehicles (SV's), civil modes of navigation signals generatedby ground and air beacons generated by pseudolites, in the presence oflarge numbers of malicious tonal and narrowband jammers; malicioussignals attempting to spoof those signals; and time and frequencyselective multipath induced by natural reflections or maliciousrepeaters. The system can operate without prior knowledge of, or asearch over, the ranging codes for those signals, and even if thosesignals are received at widely separated power levels; and perform thisdifferentiation based only on the time, frequency, and code diversitybetween those signals.

In one aspect, the multi-subband channelization architecture is extendedto spatial and/or polarization diverse multi-feed reception systems, inwhich each subband employs linear combiners, and linear-algebraiccombiner adaptation algorithms, which combine data over spectral andspatial/polarization diversity dimensions to separate GNSS signals andexcise jamming interference, and then combine detection features fromeach subband over the full bandwidth of the GNSS signal. Such systemscan exploit spatial and/or polarization diversity between the truenavigation signals and the malicious spoofers and repeaters to furtherblindly detect and differentiate the navigation signals from widebandjammers, and from signals generated by closely aligned repeaters andtargeted spoofers that are attempting to match the time, frequency, andcode diversity of the navigation signals. As an added advantage, thedimension of each subband combiner can be held constant as the number ofspatial/polarization diversity dimensions grows, resulting in a lineargrowth in complexity as spatial/polarization diversity is increased.

Aspects of the disclosure described herein include a system havingidentifying means comprising at least one antenna, coupled to at leastone receiver receptive to energy in a band containing at least onenavigation signal with an MOS-DSSS modulation format. The identifyingmeans can include a receiver, for example, dedicated or software-definedradio resources, and a digital signal processor (DSP) (e.g., DSP FPGA,GPU, or the like, with associated storage capability), or combinationsof DSP hardware configured for implementing software or firmwareinstalled on that DSP hardware. In these aspects, reception operationscan comprise:

-   -   receiving and amplifying at least one signal-in-space (SiS)        containing at least a subband of the at least one navigation        signal, comprising at least one signal with a MOS-DSSS        modulation format comprising a baseband signal with symbol rate        f_(sym), spread by a ranging code that repeats every baseband        symbol;    -   frequency-shifting the at least one SiS to an intermediate or        complex baseband frequency, e.g., using a direct-conversion        mixer with LO frequency f_(R) and appropriate filtering        operations; and    -   sampling the frequency-shifted SiS using an analog-to-digital        convertor (ADC) with a sampling rate f_(ADC) that is equal to an        integer multiple of the baseband symbol rate f_(sym), i.e.,        f_(ADC)=M_(ADC)f_(sym), where M_(ADC) is a (typically large)        integer.        In these aspects, the DSP can perform the following operations:    -   capturing at least one sampled and frequency-shifted SiS over a        block of received data samples, and recording the approximate        reception time and reception frequency of that data block,        referred to herein as a “time/frequency stamp”;    -   channelizing the sampled received data block using at least one        symbol-rate synchronous channelizer to provide at least K_(chn)        frequency channels with output rate f_(sym), each with frequency        extent lying within the active bandwidth of the MOS-DSSS        navigation signal;    -   organizing the at least K_(chn) frequency channels into K_(sub)        subsets of frequency channels, referred to herein as subbands,        each comprising M_(sub) frequency channels;    -   in multifeed receivers, wherein multiple spatial and/or        polarization diverse antennas are coupled to M_(feed) receivers        receptive to energy in a band containing at least one navigation        signal with an MOS-DSSS modulation format, channelizing each        feed into K_(chn) frequency channels with output rate f_(sym),        organizing those frequency channels into K_(sub) subbands each        comprising M_(sub) frequency channels, and combining those        subbands across receiver feeds to form a M_(DoF)×1 vector signal        with symbol rate f_(sym) for each subband, where        M_(DoF)=M_(sub)M_(feed) is referred to herein as the degrees of        freedom (DoF's) of the subband, and where M_(DoF)=M_(sub) for        the single-feed receiver (M_(feed)=1);    -   collecting the K_(sub) subbands of M_(DoF)×1 data vectors over        N_(sym) symbols, and adding a time and frequency stamp those        collections of symbols, to form a time/frequency stamped        multi-subband output data block;    -   obtaining third-party baseband symbol data or navigation data        from time channels and frequency bands covering the        time/frequency stamp, including uncertainty between the receiver        LO, clock rate, and/or clock timing phase and universal time        coordinates (UTC), using external resources also available to        the system; and    -   processing the time/frequency stamped multi-subband output data        block to obtain RPNT analytics, using blind adaptive processing        operations responsive to at least one navigation signal received        by the system, and using the third-party baseband symbol data or        navigation data.        In some aspects of the disclosure, the sampled receive data        block, or the channelized received data block, along with its        time/frequency stamp, might be transported to additional DSPs        for processing to obtain the RPNT analytics. These additional        DSPs may be onboard the platform containing the reception means,        or in a different location entirely, including infrastructure        equipment, i.e., “in the Cloud,” if the platform possesses        communications means allowing those data blocks to be        transported from the platform.

In some aspects, the reception operations are instantiated usingpurpose-built hardware and DSP hardware. In other aspects, the receptionoperations are instantiated using general-purpose software-defined radio(GPSDR) and DSP hardware. In either aspect, the receiver clock may beadjusted to remove error from UTC, once a PNT solution is obtained forthe receiver. Alternately, the ADC output data may be frequency-sampledand resampled to conform to UTC using algorithms implemented in DSPhardware, once that solution is obtained.

In the various aspects, the ADC sampling rate need not have any relationto the chip-rate of the navigation signal; nor need it have any relationto the bandwidth of the navigation signal. In particular, it can have avalue that is easily instantiated in low-cost, general-purpose, receiverhardware; and it can have a value that is substantively less than thebandwidth of the navigation signal.

In one aspect of the disclosure, the symbol-rate synchronous subbandgeneration is performed by first applying an M_(ADC)-sample fast Fouriertransform (FFT) to each S/P output data vector on each of M_(feed)receiver feeds, and then selecting K_(FFT) output bins lying within theactive bandwidth of the MOS-DSSS navigation signal, to create K_(chn)frequency channels each with output rate f_(sym) and dimensionalityM_(feed)×1. These M_(feed)×1 dimensional frequency channels are thenorganized into K_(sub) subbands with M_(sub) channels per subband,creating K_(sub) subband signals with output sampling rate f_(sym) anddimension M_(DoF)×1, where M_(DoF)=M_(sub)M_(feed). In another aspect ofthe disclosure, the subband generation is performed by passing the ADCoutput signals provided by each of M_(feed) receiver feeds through abank of K_(sub) frequency converters and decimators, each with decimatedoutput sampling rate f_(dec)=M_(dec)f_(sym), and then passing eachdecimated signal through a symbol-rate synchronous channelizer toproduce a separate M_(sub)×1 subband signal with sampling rate f_(sym),on each feed, and then “stacking” those signals to generate a M_(DoF)×1vector signal with sampling rate f_(sym), where M_(DoF)=M_(sub)M_(feed)However, the channelizer output data may be generated using manydifferent channelizer structures.

The DSP software can implement algorithms that exploit baseband symbolsequences or navigation data provided by external or “third-party”resources, for each navigation signal of interest to the system, toefficiently obtain RPNT analytics without the need to demodulate thenavigation data. Exemplary RPNT analytics can include:

-   -   estimates of observed received parameters of navigation signals,        including signal geo-observables usable to obtain PNT solutions        for the reception platform, e.g., observed signal        frequency-of-arrival (FOA), time-of-arrival (TOA), and observed        local direction-of-arrival (DOA) or global line-of-bearing (LOB)        in systems employing multi-feed receivers;    -   estimates of received signal quality, e.g., received incident        power, and of despread/demodulated navigation sequence quality,        e.g., despreader output signal-to-interference-and-noise ratio        (SINR); and    -   measures of accuracy of parameter and signal quality estimates.        RPNT analytic measurement methods include “partially-blind”        methods that do not require knowledge of the ranging code for        the navigation signals or spatial/polarization array-manifold        data (measurement of cross-feed spatial/polarization signatures        as a function of DOA) for the receiver, and “copy-aided” methods        that may require one or both of the ranging codes or the array        manifold to provide more complete RPNT analytics.

In some aspects, referred to herein as “multi-subband” systems, theblind pilot-exploiting adaptive detection and geo-observable estimationDSP algorithm can be implemented over multiple contiguous ornon-contiguous channelizer subbands. Within each subband, the method candetect and separate signals without knowledge of the spreading code; inthe presence of arbitrary channel multipath, tonal and narrower-bandjammers; and in the presence of near-far interference that is muchhigher than the spreading gain of conventional PNT systems. The methodthen combines the subbands to provide a detection statistic andgeo-observable estimate that exploits the full bandwidth of the system.The method can also provide a natural means for rejecting narrowbandjamming, such as by simply “de-emphasizing” subbands containingexcessive interference energy. As part of the FOA estimation step, themethod may also compute the differential FOA between subbands, therebyallowing direct estimation of the observed transmitter speed. In aspectswhere multiple navigation signal transmitter ephemeres are available,the method can provide a full PNT solution based on this informationalone.

In one aspect, the DSP algorithms can be implemented over multipleportions of the navigation signal band, referred to herein as“navigation signal subbands.” The navigation signal subbands can beobtained using combinations of analog and digital processing. Forexample, off-center subbands can be obtained by frequency-shifting theSiS with frequency shift f_(R) that differs substantively from thenavigation signal transmit frequency, and sampling the frequency-shiftedSiS using an ADC with a sampling rate that is much lower than thebandwidth of the navigation signal. Alternately, off-center subbands canbe obtained by downconverting, sampling, and frequency-channelizing thenavigation signal over its full bandwidth, and then selecting subsets offrequency channels to for each subband. In both cases, the subbands areprocessed using the adaptive detection, geo-observable estimation, and(for blind methods) symbol stream estimation DSP algorithms describedherein. Any combination of methods spanning this range of methods can besimilarly employed.

If the number of channelizer DoF's in each subband is greater than thetotal number of MOS-DSSS signals (e.g., legitimate navigation signals,spoofers, and substantively time and/or frequency offset multipathimages), and tonal interferers in the subband, plus additionalprocessing gain needed to integrate the pilot signal above thenon-MOS-DSSS noise-and-interference power level (not limited by thejamming margin of the ranging code), then some aspects of the disclosurecan be used to detect and determine geo-observables of all of theMOS-DSSS navigation signals covering that subband without knowledge ofthe spreading code. Moreover, aspects of the disclosure can be used toperform this detection and geo-observables estimation in the presence ofnear-far interference that is much higher than the spreading gain ofconventional PNT systems, even given the much narrower bandwidth of thesingle-subband system. In some use scenarios, e.g., reception ofnavigation signals transmitted from ground or air beacons, where thesignal RIP's are at or near the noise level, little or no additionalprocessing gain is needed to detect the navigation signals, and M_(DoF)can be much less than the spreading gain of the navigation signals. Atthe same time, the number of baseband symbols needed to obtain a usefuldetection solution can be greatly reduced by minimizing M_(DoF).Consequently, this aspect can sharply reduce the complexity of the DSPalgorithms, and the susceptibility of the method to “signature blur”induced by motion of the signal transmitters and receivers over the datacollection interval.

In some aspects, the navigation signal subbands covered by thechannelizer is also dynamically adjusted between collection intervals,e.g., by “stepping” the channelizer through multiple navigation signalsubbands, randomly moving the channelizer to different subbands duringdifferent collection intervals, or re-tasking the channelizer based onmetrics computed during prior collections. This can further reducesusceptibility of the system to narrowband or partial-band jammersattempting to block a portion of the navigation signal band, perhaps alarge portion of the band.

In one aspect, dynamic adjustment of the channelizer band is used toidentify and remove ambiguities in the FOA estimates provided by thesystem, based on differential Doppler shift between widely-spacednavigation signal subbands. For example, assuming a 1.2 kilometer/secondobserved SV speed, the GPS L5 short civil signal can experience a 40 Hzdifference in Doppler shift over its ˜10 MHz bandwidth (80 Hz if the 20MHz null-to-null bandwidth is assumed), which is well within theresolution capabilities of the method over 1-to-4 second collectintervals, and is sufficient to estimate the observed SV speed, andthereby resolve the 1 kHz FOA ambiguity induced by the 1 ksps basebandsymbol rate of this signal. In aspects where multiple navigation signaltransmitter ephemeres (time varying position, velocity, acceleration,and transmission time in universal time coordinates) are available,e.g., determined from demodulated navigation data or external resources,methods can provide a full PNT solution based on this information alone.

The DSP detection and geo-observable estimation algorithm can extendwithout qualitative change to scenarios in which the receiver possessesM_(feed)≥1 spatial/polarization diverse receive feeds, except that thechannelizer DoF's are multiplied by the number of receive feeds, suchthat M_(DoF)=M_(chn)·M_(feed), where M_(chn) is the number of channelsper feed. However, the resultant system can additionally exploitspatial/polarization diversity of MOS-DSSS signals, including targetspoofers that closely emulate the time, frequency, and code diversity ofthe legitimate navigation signals, and can further excise up toM_(feed)−1 wideband jammers, on the basis of said spatial/polarizationdiversity, even if those jammers are much stronger than the legitimatenavigation signals. As in single-feed aspects, the total DoF's mustadditionally be greater than at least the number of MOS-DSSS signals(e.g., legitimate navigation signals and spoofers) and tonal signalsimpinging on the receiver, over the bandwidth used by the system.

In one aspect of the disclosure, M_(chn)≈M_(DoF)/M_(feed), such thatM_(DoF) is held constant as the number of feeds is increased. This canfurther reduce susceptibility of the system to signature blur andprovide enhanced rejection of jammers and targeted spoofers attemptingto match the time, frequency, and code diversity of legitimatenavigation signals, even if those jammers or spoofers are much strongerthan the legitimate navigation signals.

In another aspect of the disclosure, a multi-subband channelizer withK_(sub) subbands is implemented on each receiver feed, and M_(chn) andK_(sub) are simultaneously set to M_(chn)≈M_(DoF)/M_(feed) andK_(sub)≈M_(DoF)·M_(feed), such that both M_(DoF) and the total bandwidthused by the system are held constant as the number of feeds is grown.Assuming the constraints on M_(DoF) and M_(feed) given above, theresultant system can achieve the full processing gain of the navigationsignal modulation format, and the robustness to near-far interferenceexhibited by the method in any reception scenario, without undulyaffecting complexity or convergence time of the system.

In some aspects of the disclosure, copy-aided post-processinggeo-observable estimation methods, along with ranging code informationdetermined from demodulated navigation data or through externalresources, are used to resolve the FOA and TOA ambiguities. In systemsemploying multi-feed receivers, further aspects can use the directionalarray manifold of the receiver to determine the direction of arrival(DOA) of the received signals; the receiver orientation; and truelines-of-bearing (LOB's) from the receiver to the signal emitters. Inboth aspects, the fine geo-observables can be used to geolocate spoofersidentified by the system, using known location of the receiver andgeo-observables of those spoofers.

In another aspect of the disclosure, the system employs additionalnetwork communication methods to allow intercommunication of parametersbetween multiple receivers. These receivers can employ combinations ofsingle-feed or multi-feed receivers, and can have different ADC ratesand channelization methods, as long as each channelizer provides avector sequence at a 1 ksps output data rate. Among other advantages,this aspect provides additional means for detecting and defeating targetspoofers, by using additional network diversity to prevent targetedspoofers from overwhelming any single receiver in the environment.

Any of these aspects can demodulate civil navigation signals in thepresence of arbitrary multipath because they do not explicitly exploitthe PRN code in the demodulation process. Any of these aspects canprovide for determining the yaw-pitch-roll orientation of the receiveplatform, such as due to relationship between Doppler shift anddirection vectors to the GNSS emitters, once the GNSS emitter andreceiver positions are determined.

In networked receiver configurations, intercommunication can allow eachreceiver to continuously draw from and update a “network database”containing estimated TOA's, FOA's, and (for multi-feed receivers) DOA'sfor navigation signals detected by any receiver in the network, andcontaining ephemeris information for those receivers. This database canbe used to further identify spoofers, including targeted spoofers, basedon differential FOA (DFOA) and TOA (DTOA) measured at those receivers,which removes any deliberate timing or frequency shift used by thespoofer to emulate a true navigation signal at a specific victimreceiver. If the victim receiver does not employ a multi-feed receiver,and may therefore find itself being successfully spoofed by a targetedattack, this network will provide an unambiguous alert to such anattack, as the spoofed signals will not possess the true GNSS FOA or TOAat the other receivers in the network, and will therefore be removedusing the blind adaptive despreading methods employed in aspects of thedisclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

Block diagrams and flow diagrams depicted herein can represent computersoftware instructions or groups of instructions. One or more of theprocessing blocks or steps may be implemented with modules (e.g.,procedures, functions, and so on) that perform the functions describedherein. The software codes may be stored in non-transitorycomputer-readable memory. Alternatively, processing blocks or stepsdescribed herein may represent steps performed by hardware, includingone or more functionally equivalent circuits, such as a digital signalprocessor, an application specific integrated circuit, a programmablelogic device, a field programmable gate array, a general-purposeprocessor programmed to perform one or more of the disclosed steps, orother electronic units designed to perform the functions disclosedherein. Disclosed aspects can employ multiple processors communicativelycoupled together, and can employ distributed computing, such as Cloudcomputing, cluster computing, distributed computing, etc.

FIG. 1 depicts a system in which aspects of the disclosure can beimplemented.

FIG. 2 illustrates operating parameters and geo-observables that can beemployed in aspects disclosed herein.

FIG. 3 is a block diagram that depicts generation of civil navigationsignals that aspects of the disclosure can be configured to exploit.

FIG. 4 is a Table of civil GNSS modulation formats that aspects of thedisclosure can be configured to exploit.

FIG. 5A, FIG. 5B, FIG. 6A, and FIG. 6B are block diagrams of receiverfront-ends that can be configured according to aspects of thedisclosure.

FIG. 7 is a block diagram that depicts a single-feed channelizer inaccordance with an aspect of the disclosure.

FIG. 8 is a block diagram that depicts a single-feed FFT-basedchannelizer in accordance with an aspect of the disclosure.

FIG. 9 is a block diagram of a single-feed FFT-based symbol-ratesynchronous multi-subband channelizer according to an aspect of thedisclosure.

FIG. 10 is a block diagram of a single-feed polyphase filter basedsymbol-rate synchronous multi-subband channelizer according to an aspectof the disclosure.

FIG. 11 is a block diagram of single-feed symbol-rate synchronousmulti-subband channelizer according to another aspect of the disclosure.

FIG. 12A and FIG. 12B depict exemplary channelizer metrics for arectangularly windowed polyphase filter based symbol-rate synchronouschannelizer.

FIG. 13 is a block diagram that depicts a multifeed receiver andchannelizer in accordance with an aspect of the disclosure.

FIG. 14 is a block diagram of a multifeed FFT-based symbol-ratesynchronous multi-subband channelizer according to an aspect of thedisclosure.

FIG. 15 is a block diagram of a multifeed polyphase filter basedsymbol-rate synchronous multi-subband channelizer according to an aspectof the disclosure.

FIG. 16 and FIG. 17 illustrate despreader parameters that can beemployed in aspects disclosed herein.

FIG. 18 is a flow diagram of a multi-subband signal detection,geo-observable/quality estimation, and symbol estimation algorithm thatcan be employed in aspects disclosed herein.

FIG. 19 is a flow diagram of a multi-subband signal detection andgeo-observable/quality estimation, algorithm that can be employed inaspects disclosed herein.

FIG. 20 is a flow diagram of a multi-subband signal detection andgeo-observable/quality estimation, algorithm that can be employed inaspects disclosed herein.

FIG. 21 is a flow diagram of a local-maxima search procedure accordingto an aspect of the disclosure.

FIGS. 22A, 22B, and 22C and FIGS. 23A, 23B, and 23C FIG. 22 and FIG. 23are plots that depict DFOA search sensitivity.

DETAILED DESCRIPTION

Various aspects of the disclosure are described below. It should beapparent that the teachings herein may be instantiated in a wide varietyof forms and that any specific structure, function, or both beingdisclosed herein are merely representative. Based on the teachingsherein one skilled in the art should appreciate that an aspect disclosedherein may be implemented independently of any other aspects and thattwo or more of these aspects may be combined in various ways. Forexample, an apparatus may be implemented or a method may be practicedusing any number of the aspects set forth herein. In addition, such anapparatus may be implemented or such a method may be practiced usingother structure, functionality, or structure and functionality inaddition to or other than one or more of the aspects set forth herein.

In the following description, for the purposes of explanation, numerousspecific details are set forth in order to provide a thoroughunderstanding of the invention. It should be understood, however, thatthe particular aspects shown and described herein are not intended tolimit the invention to any particular form, but rather, the invention isto cover all modifications, equivalents, and alternatives falling withinthe scope of the invention as defined by the claims.

FIG. 1 depicts a model of the presumed normal condition wherein areceiver (1) is receiving GPS signals from an SV (3).

FIG. 2 Illustrates exemplary observable parameters of signalstransmitted from a GNSS SV (3) to a GNSS receiver (1) that can be usedto geo-locate those signals (“geo-observables”) (6), as a function ofparameters local to the GNSS SV (4) and the GNSS receiver (2). Thesegeo-observables (6) include the time-of-arrival (TOA) (after removal ofdelays induced in transmitter and receiver electronics), receivedincident power (RIP), line-of-bearing (LOB), direction-of-arrival (DOA)relative to the platform orientation, frequency-of-arrival (FOA) (afterremoval of known frequency offset between the transmitter and receivercenter frequencies), and carrier phase (CCP) (e.g., after calibrationand removal of transmitter and receiver phase offsets), which aremeasurable and differentiable at the receiver (1).

The TOA, RIP, FOA, LOB, DOA, and CCP are referred to as geo-observable,as they are observable parameters of the GNSS received signals that canbe used to geo-locate the GNSS receiver, given knowledge of the GNSStransmitter locations over time, which are transmitted within thenavigation stream of those signals. They are also referred to here aspositioning, navigation, and timing (PNT) analytics, as they providemetadata of the transmitted signals that can be used for purposes beyondgeo-location of the receiver, e.g., to assess quality and reliability ofthe received GNSS signals, in order to aid other PNT systems on boardthe receiver platform.

FIG. 3 depicts operations used to generate the civil navigation signalsthat are the focus of the invention. It should be noted that theprocessing steps shown in FIG. 3 is one conceptual means for generatingcivil GNSS signals, and ignore other SiS's that may be transmittedsimultaneously with civil GNSS signals, for example, the GPS P, P(Y), M,and L1C SiS's. In practice, these other SiS's are largely outside theband occupied by the civil GNSS signals, and moreover are received wellbelow the noise floor. Therefore, their effect on aspects describedherein is small. An important exception is military GNSS signals thatmay be generated by terrestrial pseudolites, as the non-civil componentsof those signals may be above the noise floor within the civil GNSSpassband in some use scenarios.

The processing steps shown in FIG. 3 generate a particular class ofspread spectrum signal, referred to herein as a modulation-on-symboldirect-sequence spread spectrum (MOS-DSSS) signal, in which a datasymbol sequence d_(T)(n_(sym);l) with symbol rate f_(sym) is spread by aM_(chp)×1 dimensioned ranging code

c_(T)(ℓ) = [c_(T)(m_(chp); ℓ)]_(m_(chp) = 0)^(M_(chp) − 1)that is repeated over every data symbol. The spread signal can berepresented as the multiplication of data symbol sequenced_(T)(n_(sym);l) and code vector c_(T)(l) (115), resulting in M_(chp)×1c_(T) (l)d_(T)(n_(sym);l). The vector signal is then passed through aM_(chp):1 parallel-to-serial (P/S) converter (116), resulting in ascalar spread signal with rate M_(chp)f_(sym), which can be expressed asc_(T)(n_(chp) mod M_(chp);l)d_(T)(└n_(chp)/M_(chp)┘;l) where (⋅)mod Mand └⋅┘ denote the modulo-M operation and integer truncation or “floor”operations, respectively. As shall be described below, this propertyinduces inherent massive spectral redundancy to the civil GNSS formatthat is exploited by disclosed aspects.

The chip-rate spread signal is then passed through digital-to-analogconversion (DAC) (118), and transmission/upconversion stages (120),controlled by an internal clock (clk) (117) and local-oscillator (LO)(119) stages, and transmitted from an antenna (121) to generate asignal-in-space (SiS) given by √{square root over(2P_(T)(l))}Re{s_(T)(t−τ_(T)(l);l)e^(j(2πd) ^(T) ^(t+φ) ^(T) ^((l)))}for transmitter l (122), where f_(T)(l) is the transmit frequency,typically common to all SV's (f_(T)(l)≡f_(T)), P_(T)(l), φ_(T)(l) andτ_(T)(l) are the transmit power, phase, and electronics delay for SiS l,respectively, and where s_(T)(t;l) is the complex basebandrepresentation of the transmitted signal.

Based on these operations, the complex-baseband signal can be modeled by

$\begin{matrix}{{{s_{T}\left( {t;\ell} \right)} = {\sum\limits_{n_{sym}}{{d_{T}\left( {n_{sym};\ell} \right)}{h_{T}\left( {{t - {T_{sym}n_{sym}}};\ell} \right)}}}},} & {{Eqn}(1)}\end{matrix}$where d_(T)(n_(sym);l) is the encoded symbol stream, T_(sym)=1/f_(sym),is the symbol period, and h_(T)(t;l) is a spread symbol given by

$\begin{matrix}\begin{matrix}{{{h_{T}\left( {t;\ell} \right)} = {\overset{M_{chp} - 1}{\sum\limits_{m_{chp} = 0}}{c_{T}\left( {m_{chp};\ell} \right)g_{T}\left( {{t - {T_{chp}m_{chp}}};\ell} \right)}}},} & {{T_{chp} = \frac{T_{sym}}{M_{chp}}},}\end{matrix} & {{Eqn}(2)}\end{matrix}$and where g_(T) (t;l) is the chip symbol modulated by each chip,referred to here as the chip shaping. The spread symbol can also beexpressed by it's continuous Fourier transformH_(T)(f;l)=∫h_(T)(f;l)e^(−j2πft) df,H _(T)(f;l)=C _(T)(e ^(j2πfT) ^(chp) ;l)G _(T)(f;l),  Eqn (3)where

${C_{T}\left( {e^{j2\pi f};\ell} \right)} = {\sum\limits_{m_{chp}}{{c_{T}\left( m_{chp} \right)}e^{{- j}2\pi{fm}_{chp}}}}$is the discrete Fourier transform of C_(T)(m_(chp);l), and whereG_(T)(f;l) is the continuous Fourier transform of g_(T)(t;l). The spreadsignal can therefore be modeled as a pulse-amplitude modulated (PAM)waveform in which baseband symbol sequence modulates a symbol waveformthat is itself direct-sequence spread by the ranging code, leading tothe MOS-DSSS nomenclature employed here.

In typical navigation systems, the chip shaping is identical for eachtransmitted signal (g_(T)(t;l)≡g_(T)(t)); however, in practice, theshaping can also vary between transmitters. For typical navigationsystems, the chip shaping is also nominally rectangular, such thatG_(T)(f;l)≡T_(chp)Sa(πfT_(chp)), where Sa(x)=sin(x)/x; however,different chip shapings can be employed without changing the basicstructure of the MOS-DSSS modulation format.

In typical navigation systems, the spreading code C_(T)(l) employed attransmitter l is unique to that transmitter, and is in fact provisionedby the navigation system. In contrast, the transmit power and centerfrequency are typically (but not necessarily) identical for eachtransmitter, while the transmitter carrier phase, delay, and otherimpairments will vary between the transmitters. However, any of thesetypical assumptions can be varied in practice, or in differentinstantiations of a navigation system.

As shown in FIG. 3 , the full symbol sequence d_(T)(n_(sym);l) isgenerated from an underlying navigation sequence b_(T)(n_(NAV);l)|_(NAV)with navigation rate f_(NAV), which contains information needed togenerate a full positioning, navigation, and timing (PNT) solution atnavigation receiver. The navigation sequence typically provides timingand ephemeris (time-stamped position, velocity, and acceleration) of thenavigation transmitter and larger network, known impairments at thetransmitter, and additional information needed to determine quality andtiming of the transmitted signal. The navigation sequence also typicallyprovides information about the specific spreading code(s) employed atthe transmitter. This navigation sequence is then passed throughprocessing operations to generate an encoded signal sequenceb_(T)(n_(sym);l)|_(sym), with symbol rate f_(sym) and for somemodulation formats combined with a known pilot sequencep_(T)(n_(sym);l), with symbol rate f_(sym) (112 b) to generate the fullsymbol sequence signal d_(T)(n_(sym);l). All of these additionalprocessing steps add additional known structure to the transmittedMOS-DSSS signal, which can be exploited in subsequent processing stages.Additionally, the navigation sequence, the information contained withinthat sequence (e.g., the transmitter ephemeres) can be obtained aftertransmission from third-party sources, providing additional exploitablestructure in applications some aspects of the invention.

FIG. 4 is a tabular description of GNSS networks employing civil GNSSsignals that can be modeled as MOS-DSSS signals. As this Figure shows,every GNSS network deployed to date possesses at least one signal typethat can be modeled by FIG. 3 . Moreover, all of these signals have a 1millisecond (ms) ranging code period, and therefore a 1 ksps (kilosampleper second) MOS-DSSS baseband symbol rate, albeit with widely varyingchip rates and SiS bandwidths, allowing their demodulation using acommon receiver structure.

As the last column of FIG. 4 shows, the symbol streams of each of thesesignals possess properties that can be used to detect and differentiatethem from other signals in the environment, including military GNSSsignals, jammers, and civil GNSS signals with the same or similarproperties. For example, the GPS coarse acquisition (C/A) or “legacy”signal listed in the first row of FIG. 4 is constructed from a 50bit/second (bps) BPSK (real) navigation sequenceb_(T)(n_(NAV);l)|_(NAV), repeated 20 times per MOS-DSSS symbol togenerate 1 ksps symbol sequenced_(T)(n_(sym);l)=b_(T)(n_(sym);l)|_(sym)=b_(T)(└n_(sym)/M_(NAV)┘;l)|_(NAV)where M_(NAV)=20. Moreover, b_(T)(n_(NAV);l)|_(NAV) possesses internalfields that can be further exploited to aid the demodulation process,e.g., the TLM Word Preamble transmitted within every 300-bit Navigationsubframe.

Similarly, the GPS L5, QZSS, Galileo E5B, E6B, and Beidou 1Btransmitters all add a periodic pilot to the quadrature rail of theirnavigation signals, and the NAVIC RS BOC transmitter adds a periodicpilot to the in-phase rail of its navigation signal. Means forexploiting periodic pilots are a focus of some aspects of thisinvention.

FIG. 5A and FIG. 5B each depict exemplary direct-conversion front-endreception processing for a single-feed receiver receiving GNSS signals.FIG. 5A shows a direct-conversion receiver front-end that is dedicatedto a specific GNSS band, and FIG. 5B shows a direct-conversion receiverfront-end that can be flexibly tasked to any GNSS band, consistent witha software defined radio (SDR) architecture. Each can be used as a partof, and in, some of the disclosed aspects.

The direct-conversion receivers shown in FIG. 5A and FIG. 5B eachcomprise the following:

-   -   An antenna (128) and low-noise amplifier (LNA) (131), which        receives an SiS containing GNSS emissions within the FoV of the        receiver.    -   A local oscillator (LO) (133), which generates a complex        sinusoid with frequency f_(R) and phase φ_(R), comprising an        in-phase (I) real sinusoid, and a quadrature (Q) sinusoid        shifted by 90° in phase from the in-phase sinusoid;    -   A complex mixer (134), which multiplies the LNA output signal by        the conjugate of the complex sinusoid, thereby creating a        complex signal with real and imaginary parts, referred to herein        as the in-phase (I) and quadrature (Q) rails of that signal,        which has been downconverted by frequency shift f_(R)    -   A dual lowpass filter (LPF) (135), which filters each signal        rail to remove unwanted signal energy from the complex        downconverted signal, yielding analog scalar complex-baseband        signal x_(R)(t), centered at 0 MHz if f_(R)=f_(T).    -   A dual analog-to-digital converter (ADC) (136), which samples        each rail of x_(R)(t) at rate f_(ADC)=M_(ADC)f_(sym), where        f_(sym) is the civil GNSS signal symbol rate shown in FIG. 3 and        M_(ADC) is a positive integer, thereby generating complex        dual-ADC output signal x_(ADC)(n_(ADC)) with time index n_(ADC)        (137).        The receiver structure shown in FIG. 5A possesses an additional        bandpass filter (BPF) (130), inserted between the antenna and        LNA, and dedicated to a specific GNSS band, which removes        unwanted adjacent-channel interference (ACI) from the received        GNSS SiS, and depicts an LO that is locked to specific, preset        value, consistent with a dedicated receiver that is optimized        for a specific GNSS band. This structure is more typical of        existing GNSS receivers, and provides enhanced signal quality at        cost of receiver flexibility.

In contrast, the receiver structure shown in FIG. 5B is consistent withSDR receivers that can be tasked to any GNSS band under user control.This receiver structure can also be used to receive a segment of a GNSSband, e.g., a 1 MHz segment of the GPS L5 band, if f_(R) issignificantly offset from the GNSS band center f_(T). The ability toblindly detect, demodulate, and estimate geo-observables of any portionof any GNSS band using the same reception, downconversion, and samplinghardware regardless of the actual bandwidth of the GNSS signals presentin that band can be an advantageous feature of at least some of thedisclosed aspects.

FIG. 6A and FIG. 6B each depict exemplary front-end reception processingfor a single-feed superheterodyne receiver receiving GNSS signals; withFIG. 6A showing a superheterodyne receiver front-end that is dedicatedto a specific GNSS band, and FIG. 6B showing a superheterodyne receiverfront-end that can be flexibly tasked to multiple GNSS bands. Each canbe used as a part of, and in, at least some aspects disclosed herein.

The heterodyne receivers shown in FIG. 6A and FIG. 6B shift the SiSreceived by an antenna (128) and amplified in an LNA (130) to IFfrequency f_(IF), typically using a two-stage mixer 134, 141, yieldinganalog scalar real-IF signal x_(R)(t) centered on IF frequency f_(IF) iff_(R)=f_(T), with receive phase-shift φ_(R)=φ_(R) ⁽¹⁾+φ_(R) ⁽²⁾. Theanalog signal is then passed to an ADC (143) that samples x_(R)(t) atrate M_(ADC)f_(sym), where f_(sym) is the MOS-DSSS signal symbol rateshown in FIG. 6A and FIG. 6B, and M_(ADC) is a positive integer,yielding real ADC output signal X_(ADC)(n_(ADC)) with time index n_(ADC)(137). The receiver structure shown in FIG. 6A can be optimized for aspecific GNSS band, while the receiver structure shown in FIG. 6B can beflexibly tasked to different navigation signal bands, or to segments ofsuch bands, under software control.

In all four cases, the receiver can induce additional delays, frequencyoffsets, and sampling rate offsets due to internal electronics in thereceiver systems, and due to clock rate and timing offset from universaltime coordinates (UTC). These are subsumed into the overall channelresponse, and measured and removed as part of the geo-location solution.

As will be discussed below, the ADC output signal provided by either thedirect-conversion or the superheterodyne receivers can be used indisclosed aspects without any change to the design, except controlparameters used in channelization operations immediately after that ADC.The disclosed aspects can also be practiced with many other receiverfront-ends known to the art. In many cases, the disclosed aspects areblind to substantive differences between those receiver front-ends.

Assuming the reception scenario shown in FIG. 2 , and thedirect-conversion receiver structure shown in FIG. 5 , the downconvertedand filtered signal shown in x_(R)(t) is given by

$\begin{matrix}{{{x_{R}(t)} = {{i_{R}(t)} + {\overset{L}{\sum\limits_{\ell = 1}}{s_{R}\left( {t;\ell} \right)}}}},} & {{Eqn}(4)}\end{matrix}$where i_(R)(t) is the noise and interference received in the receiverpassband and s_(R)(t;l) is the complex-baseband representation of thesignal received from transmitter l. Over time intervals on the order of1-10 seconds from reception time t₀, s_(R)(t;l) can be modeled by

$\begin{matrix}{{{s_{R}\left( {{t_{0} + t};\ell} \right)} \approx {{g_{TR}(\ell)}e^{j2{\pi({{{\alpha_{TR}(\ell)}t} + {\frac{1}{2}\alpha\begin{matrix}{(1)} \\{TR}\end{matrix}{(\ell)}t^{2}}})}}{s_{T}\left( {{{\left( {1 + {\tau\begin{matrix}(1) \\{TR}\end{matrix}(\ell)}} \right)t} - {\tau_{TR}(\ell)}};\ell} \right)}}},} & {{Eqn}(5)}\end{matrix}$at the input to the dual-ADC's shown in FIG. 5 , where

$\begin{matrix}{{{g_{TR}(\ell)}\overset{\bigtriangleup}{=}{\sqrt{P_{R}\left( {t_{0};\ell} \right)}{\exp\left( {j{\varphi_{TR}(\ell)}} \right)}}},{{end}‐{to}‐{end}{complex}{channel}{gain}}} & {{Eqn}(6)}\end{matrix}$ $\begin{matrix}{{{\varphi_{TR}(\ell)}\overset{\bigtriangleup}{=}{{\varphi_{T}(\ell)} - \varphi_{R} - {2\pi{f_{T}(\ell)}{\tau_{TR}\left( {t_{0};\ell} \right)}}}},{{end}‐{to}}‐{{end}{channel}{phase}}} & {{Eqn}(7)}\end{matrix}$ $\begin{matrix}\begin{matrix}{{{\tau_{TR}(\ell)}\overset{\bigtriangleup}{=}{{\tau_{T}(\ell)} + \tau_{R} + {\tau_{TR}^{(0)}\left( {t_{0};\ell} \right)}}},} & {{end}‐{to}‐{end}{observed}{}TOA}\end{matrix} & {{Eqn}(8)}\end{matrix}$ $\begin{matrix}\begin{matrix}{{{\alpha_{TR}(\ell)}\overset{\bigtriangleup}{=}{{f_{T}(\ell)} + f_{R} - {{f_{T}(\ell)}{\tau_{TR}^{(1)}\left( {t_{0};\ell} \right)}}}},} & {{end}‐{to}‐{end}{observed}FOA}\end{matrix} & {{Eqn}(9)}\end{matrix}$ $\begin{matrix}\begin{matrix}{{{\tau_{TR}^{(1)}(\ell)}\overset{\bigtriangleup}{=}{\tau_{TR}^{(1)}\left( {t_{0};\ell} \right)}},} & {{observed}{differential}TO{A\left( {DTOA} \right)}}\end{matrix} & {{Eqn}(10)}\end{matrix}$ $\begin{matrix}\begin{matrix}{{{\alpha_{TR}^{(1)}(\ell)}\overset{\bigtriangleup}{=}{{- {f_{T}(\ell)}}{\tau_{TR}^{(2)}\left( {t_{0};\ell} \right)}}},} & {{observed}{differential}FO{{A\left( {DFOA} \right)}.}}\end{matrix} & {{Eqn}(11)}\end{matrix}$and where φ_(T)(l), f_(T)(l), and τ_(T)(l) are the carrier phase,frequency, and timing offset induced at transmitter l; φ_(R), f_(R), andτ_(R) are the carrier phase, frequency, and timing offset induced at thereceiver; P_(R)(t₀;l) is the received incident power of SiS l at thereceiver; and τ_(TR) ^((q))(t₀;l)=dτ_(TR)(t;l)/dt^(q) is the q^(th)derivative of the observed TOA between transmitter l and the receiver attime t. Given observed position, velocity, and accelerationp_(TR)(t;l)=p_(T)(t;l)−p_(R)(t;l), v_(TR)(t;l)=v_(T)(t;l)−v_(R)(t;l),and a_(TR)(t;l)=a_(T)(t;l)−a_(R)(t;l), where{p_(T)(t;l),v_(T)(t;l),a_(T)(t;l)}_(l=1) ^(L) and{p_(R)(t),v_(R)(t),a_(R)(t)} are the transmitter and receiver ephemeres,respectively, then τ_(TR) ^((q))(t;l) is given by

$\begin{matrix}{{{\tau_{TR}^{(0)}\left( {t;\ell} \right)} = {\frac{1}{c}{{p_{TR}\left( {t;\ell} \right)}}_{2}}},} & {{Eqn}(12)}\end{matrix}$ $\begin{matrix}{{{\tau_{TR}^{(1)}\left( {t;\ell} \right)} = {\frac{1}{c}{u_{TR}^{T}\left( {t;\ell} \right)}{v_{TR}\left( {t;\ell} \right)}}},} & {{Eqn}(13)}\end{matrix}$ $\begin{matrix}{{{\tau_{TR}^{(2)}\left( {t;\ell} \right)} = {\frac{1}{c}\left( {{{u_{TR}^{T}\left( {t;\ell} \right)}{a_{TR}\left( {t;\ell} \right)}} + {{{P_{\bot}\left( {p_{TR}\left( {t;\ell} \right)} \right)}{v_{TR}\left( {t;\ell} \right)}}}_{2}} \right)}},} & {{Eqn}(14)}\end{matrix}$where u_(TR)(t;l) is the line-of-bearing (LOB) direction vector from thereceiver to transmitter l,

$\begin{matrix}{{{u_{TR}\left( {t;\ell} \right)} = \frac{p_{TR}\left( {t;\ell} \right)}{{{p_{TR}\left( {t;\ell} \right)}}_{2}}},} & {{Eqn}(15)}\end{matrix}$and P_(⊥)(p_(TR)(t;l)) is the projection matrix orthogonal top_(TR)(t;l), given by

$\begin{matrix}{{{P_{\bot}\left( {p_{TR}\left( {t;\ell} \right)} \right)} = {I_{3} - \frac{{p_{TR}\left( {t;\ell} \right)}{p_{TR}^{T}\left( {t;\ell} \right)}}{{{p_{TR}\left( {t;\ell} \right)}}_{2}^{2}}}},} & {{Eqn}(16)}\end{matrix}$and where ∥⋅∥₂ and I₃ denote the L2 Euclidean vector norm and 3×3identity matrix, respectively. As shown in the '417 NPA, incorporatedherein by reference, the RIP and LOB adheres closely to a zero-ordermodel over time intervals on the order of 1-to-10 seconds, fortransmitters in medium-Earth orbits and receivers with dynamicscommensurate with high-velocity airborne vehicles.

The local direction-of-arrival (DOA) of the signal received fromtransmitter l can then be represented by local DOA direction vectoru_(R)(t;l)=Ψ_(R)(t)u_(TR)(t;l), which can be converted to azimuthrelative to the local receiver heading and elevation relative to theplane of receiver motion using well-known directional transformations.As shown in the '417 NPA, incorporated herein by reference, the DOA alsoadheres closely to a first-order model over time intervals on the orderof 1-to-10 seconds, for transmitters in medium-Earth orbits andreceivers with dynamics commensurate with high-velocity airbornevehicles. Moreover, the variation in local DOA is nearly identical forall of the received navigation signals under this scenario, as itprimarily due to motion/orientation of the receiver, which equallyaffects all of the signal LOB's.

FIG. 7 shows a single-feed receiver structure used in one aspect of thedisclosure, describing the symbol-rate synchronous vector channelizer(150) integral to the disclosure. A SiS is received at an antenna (128),and downconverted to complex baseband using a direct-conversion receiver(100) implementing operations such as those shown in FIG. 5A and FIG.5B, comprising reception, frequency downconversion by receive frequencyf_(R) to complex baseband representation, and sampling using a dual ADC(136) with sampling rate M_(ADC)f_(sym), where M_(ADC) is a positiveinteger. The sampled signal is then passed to a symbol-rate synchronouschannelizer (150) comprising the following conceptual operations:

-   -   A 1:M_(ADC) serial-to-parallel conversion operation that        transforms the rate M_(ADC)f_(sym) ADC output signal to an        M_(ADC)×1 vector signal x_(sym)(n_(sym)) with rate f_(sym),        given by

$\begin{matrix}{{x_{sym}\left( n_{sym} \right)} = {\begin{pmatrix}{x_{R}\left( {T_{sym}n_{sym}} \right)} \\ \vdots \\{x_{R}\left( {T_{sym}\left( {n_{sym} + \frac{m_{ADC}^{- 1}}{M_{ADC}}} \right)} \right)}\end{pmatrix}.}} & {{Eqn}(17)}\end{matrix}$

-   -   An M_(ADC):K_(chn) channelization operation (155), conceptually        performed by operating on x_(sym)(n_(sym)) using K_(chn)×M_(ADC)        channelization matrix operator T_(chn) (153) to form K_(chn)×1        channelizer output signal        x_(chn)(n_(sym))=T_(chn)∘x_(sym)(n_(sym)) (159), where K_(chn)        is the symbol-rate synchronous output channels used in        subsequent DSP operations and “∘” denotes a general filtering        operation. In some aspects of the invention, T_(chn) (153) is a        memoryless matrix and the operation is a simple matrix        multiplication. In other aspect of the invention, T_(chn) (153)        is a more linear-time-invariant (LTI) impulse response, and the        operation is a matrix convolution.        The data rate of x_(chn)(n_(sym)) is nominally equal to the        symbol rate of the navigation signal of interest to the system        (less offset due to nonideal error in the ADC clock), e.g., 1        ksps for the signals listed in FIG. 4 , and the dimensionality        of x_(chn)(n_(sym)) is K_(chn)×1, where K_(chn) Is the number of        frequency channels used by subsequent DSP processing stages.        Hence this is referred to here as a symbol-rate synchronous        vector channelizer.

A variety of different channelization methods can be implemented usingthis general processing structure, including time and frequency domainchannelization methods, or channelizations employing mixedtime-frequency channelizations such as wavelet-based channelizers.

FIG. 8 depicts a specific instantiation of the symbol-rate synchronousvector channelizer (150), using Fast-Fourier Transform (FFT) operations.The channelizer first applies a (nominally zero-padded) discrete Fouriertransform (DFT) with M_(ADC) input samples, K_(FFT)≥M_(ADC) output bins(152), and a (nominally rectangular) window

$\begin{matrix}\left\{ {w_{chn}\left( m_{ADC} \right)} \right\}_{m_{ADC} = 0}^{M_{ADC} - 1} & (156)\end{matrix}$to each S/P output vector, where K_(FFT) can be conveniently chosen tominimize computational complexity and/or cost of the DFT using an FFTalgorithm. The channelizer then selects K_(chn) output bins

{k_(bin)((k_(chn))}_(k_(chn) = 0)^(K_(chn) − 1)for use in subsequent adaptive processing algorithms (154). Thechannelization operation can be expressed as a multiplication ofx_(sym)(n_(sym)) by K_(chn)×M_(ADC) matrix

$\begin{matrix}{T_{chn} = {\left\lbrack {{\exp\left( {{- j}2\pi{k_{bin}\left( k_{chn} \right)}\frac{m_{ADC}}{K_{FFT}}} \right)}{w_{chn}\left( m_{ADC} \right)}} \right\rbrack.}} & (153)\end{matrix}$

In one aspect of the invention, the output channelizer bins are selectedcontiguously over the passband of the receiver, e.g., using formulak_(bin)(k_(chn))=(k_(init)+k_(chn))mod K_(FFT), where k_(init) is thefirst FFT bin output from the channelizer (FFT bin associated withchannelizer bin 0). As will be discussed herein, an advantage of thisapproach is minimization of channel signature blur due to movement ofthe transmitter and/or receiver platforms. In another aspect of theinvention, the output channelizer bins are selected sparsely over thepassband of the receiver, e.g., using formulak_(bin)(k_(chn))=(k_(init)+K_(sep)k_(chn))mod K_(FFT), where K_(sep) isan integer separation factor between channelizer bins. An advantage ofthis approach is ability to avoid known receiver impairments such as LOleakage (e.g., by setting k_(init) to a non-multiple of K_(sep)), or toreduce complexity of the channelization operation, e.g., using sparseFFT methods.

In some aspects of the invention, the output channelizer bins arepreselected, e.g., to avoid known receiver impairments such as LOleakage, or to reduce complexity of the channelization operation. Inother aspects of the invention, the output channelizer bins areadaptively selected, e.g., to avoid dynamic narrowband co-channelinterferers (NBCCI).

In, the '417 NPA, which has been incorporated herein by reference, meansfor processing the vector channelizer output signal, in that case withK_(chn)=M_(DoF). However, exploitation of channelizationdimensionalities covering the full active bandwidth of the GPS L1 legacysignal, much less the much wider bandwidth GPS L5 and other civil GNSSsignals, would substantively increase both the complexity of thelinear-algebraic methods disclosed in the '417 NPA, and the receptiontime needed to implement those methods. For this reason, the '417 NPAfocused on partial-band and subband methods that only exploited a partof that active bandwidth. Methods for overcoming this limitation withoutunduly affecting complexity or reception time is a primary focus of thisinvention.

FIG. 9 depicts an instantiation of a single-feed FFT-based symbol-ratesynchronous multi-subband channelizer, intended to overcome theselimitations. This instantiation is identical to the FFT-basedsymbol-rate synchronous channelizer shown in FIG. 8 , except that theK_(chn)-channel selection operation (154) is replaced by a subbandselection operation (157) that selects K_(sub) subbands from the K_(FFT)FFT output bins provided by the FFT operation (152). In the aspect ofthe invention shown in this Figure, the number of bins in each subbandis equal to the same number, M_(DoF), referred to herein as the numberof degrees of freedom of the subband. This has the benefit ofregularizing linear-algebraic DSP operations performed on each subbandin subsequent processing steps. However, other aspects of the inventioncan vary the number of bins, and therefore processing degrees offreedom, e.g., based on numbers of interferers present in each subbandor other factors. The FFT output bins selected for the subbands are thenorganized into K_(sub) M_(DoF)×1 vector signals given by

$\begin{matrix}{{{x_{DoF}\left( {n_{sym};k_{sub}} \right)} = \begin{pmatrix}{x_{FFT}\left( {{k_{bin}\left( {0;k_{sub}} \right)},n_{sym}} \right)} \\ \vdots \\{x_{FFT}\left( {{k_{bin}\left( {{M_{DoF} - 1};k_{sub}} \right)},n_{sym}} \right)}\end{pmatrix}}{{k_{sub} = 0},\ldots,{K_{sub} - 1},}} & {{Eqn}(18)}\end{matrix}$each with output rate f_(sym), where

{x_(FFT)(k_(bin), n_(sym))}_(k_(bin) = 0)^(K_(FFT) − 1)are the bins output from the FFT (152).

In one aspect of the invention, the FFT bins selected for each subbandare contiguous, e.g., set using formulak_(bin)(m_(DoF);k_(sub))=(k_(init)(k_(sub))+m_(DoF))mod K_(FFT), wherek_(init)(k_(sub)) denotes the initial FFT bin selected for subbandk_(sub). As will be discussed herein, an advantage of this approach isminimization of channel signature blur due to movement of thetransmitter and/or receiver platforms. In another aspect of theinvention, the FFT bins selected for each subband are more sparselydistributed, e.g., using formulak_(bin)(m_(DoF);k_(sub))=(k_(init)(k_(sub))+K_(sep)m_(DoF))mod K_(FFT),where K_(sep) is an integer separation between bins within the subband.An advantage of this approach is ability to avoid known receiverimpairments such as LO leakage, or to reduce complexity of thechannelization operation, e.g., using sparse FFT methods. The binspacing K_(sep) can be equal for each subband, or be different betweensubbands.

In one aspect of the invention, the subband are themselves contiguous,e.g., such that k_(init)(k_(sub)+1)=(k_(init)(k_(sub))+M_(DoF))modK_(FFT) for subbands with contiguous bins within each subband, andk_(init)(k_(sub)+1)=(k_(init)(k_(sub))+K_(sep)M_(DoF))mod K_(FFT) forsubbands with sparsely separated bins within each subband. In otheraspects of the invention, subbands may be widely separated. In yet otheraspects of the invention, subbands may be interleaved, e.g., by settingK_(sep)=K_(sub) and k_(init)(k_(sub))=k_(init)(0)+k_(sub), such thatk_(bin)(m_(DoF);k_(sub))=(k_(init)(0)+(K_(sub)m_(DoF)+k_(sub)))modK_(FFT).

In some aspects of the invention, the output subband bins arepreselected, e.g., to avoid known receiver impairments such as LOleakage, or to reduce complexity of the channelization operation. Inother aspects of the invention, the output subband bins are adaptivelyselected, e.g., to avoid dynamic narrowband co-channel interferers(NBCCI).

FIG. 10 is a block diagram of an alternate single-feed polyphase filterbased symbol-rate synchronous multi-subband channelizer, according to anaspect of the disclosure. This block diagram also depicts a simple meansfor separating the channelizer output signal into contiguous subbands.The ADC output data x_(R)(T_(ADC)n_(ADC)) is passed through a 1:M_(ADC)serial-to-parallel converter (151) and a Q_(ADC)M_(ADC)-tap polyphasefilter (160) with (typically real, potentially complex) channelizerweights

$\begin{matrix}{\left\{ {w_{chn}\left( m_{ADC} \right)} \right\}_{m_{ADC} = 0}^{Q_{ADC}M_{ADC}},} & 158\end{matrix}$given by

$\begin{matrix}{{{x_{chn}\left( {k_{chn},n_{sym}} \right)} = {\sum\limits_{m_{ADC} = 0}^{{Q_{ADC}M_{ADC}} - 1}{{w_{chn}^{*}\left( m_{ADC} \right)}{x_{R}\left( {T_{ADC}\left( {{M_{ADC}n_{sym}} + m_{ADC}} \right)} \right)}e^{{- j}2\pi{f_{chn}(k_{chn})}T_{ADC}m_{ADC}}}}},} & {{Eqn}(19)}\end{matrix}$such that x_(chn)(n_(sym)) is given by

$\begin{matrix}{{{x_{chn}\left( n_{sym} \right)} = {\underset{q_{ADC} = 0}{\sum\limits^{Q_{ADC} - 1}}{{T_{chn}\left( q_{sym} \right)}{x_{sym}\left( {n_{sym} + q_{sym}} \right)}}}}{{T_{chn}\left( q_{sym} \right)} = \text{ }{\left\lbrack {{w_{chn}^{*}\left( {{M_{ADC}q_{sym}} + m_{ADC}} \right)}e^{{- j}2\pi{f_{chn}(k_{chn})}{T_{ADC}({{M_{ADC}q_{sym}} + m_{ADC}})}}} \right\rbrack.}}} & {{Eqn}(20)}\end{matrix}$Relating to FIG. 7 , this channelizer employs a transformationx_(chn)(n_(sym))=T_(chn)∘x_(sym)(n_(sym)), where T_(chn) is aK_(chn)×M_(ADC) polyphase filter with response length Q_(ADC). In theaspect shown in FIG. 10 , the channel frequencies

{f_(chn)(k_(chn))}_(k_(chn) = 0)^(K_(chn) − 1)are furthermore assumed to satisfy

$\begin{matrix}{{f_{chn}\left( k_{chn} \right)} = {\left( {k_{chn} - \frac{K_{chn} - 1}{2}} \right)f_{sym}}} & {{Eqn}(21)}\end{matrix}$such that

$\begin{matrix}{{T_{chn}\left( q_{sym} \right)} = {{\left( {- 1} \right)^{{({K - 1})}q_{sym}}\left\lbrack {{w_{chn}^{*}\left( {{M_{ADC}q_{sym}} + m_{ADC}} \right)}e^{{- j}2\pi k_{chn}{m_{ADC}/M_{ADC}}}} \right\rbrack}.}} & {{Eqn}(22)}\end{matrix}$This channelizer can be implemented using methods well-known to those ofordinary skill in the art.

If K_(chn)=K_(sub)M_(DoF), then x_(chn)(n_(sym)) can be directlytransformed to K_(sub) contiguous M_(DoF)×1 vector subband signals

{x_(DoF)(n_(sym); k_(sub))}_(k_(sub) = 0)^(K_(sub) − 1)with contiguous in-subband channels using a M_(DoF)×K_(sub) reshapingoperation (161), such that

x_(DoF)(n_(sym); k_(sub)) = [x_(chn)(M_(DoF)k_(sub) + m_(DoF), n_(sym))]_(m_(DoF) = 0)^(M_(DoF) − 1).The subband center frequencies

{f_(sub)(k_(sub))}_(k_(sub) = 0)^(K_(sub) − 1)are then given by

$\begin{matrix}{{{f_{sub}\left( k_{sub} \right)} = {\left( {k_{sub} - \frac{K_{sub} - 1}{2}} \right)M_{DoF}f_{sym}}},{k_{sub} = 0},\ldots,{K_{sub} - 1}} & {{Eqn}(23)}\end{matrix}$while the frequency channels within each subband are locally given by

$\begin{matrix}{{{f_{chn}\left( m_{DoF} \right)} = {\left( {m_{DoF} - \frac{M_{DoF} - 1}{2}} \right)f_{sym}}},{m_{DoF} = 0},\ldots,{M_{DoF} - 1}} & {{Eqn}(24)}\end{matrix}$such thatf_(chn)(M_(DoF)k_(sub)+m_(DoF))=f_(sub)(k_(sub))+f_(chn)(m_(DoF)).

FIG. 11 is a block diagram of a single-feed symbol-rate synchronousmulti-subband channelizer according to another aspect of the disclosure.In this aspect, the ADC output signal is passed through a set of K_(sub)frequency converters (162 a)-(162 b) and decimators (163 a)-(163 b),each of which frequency downconverts the ADC output signal by frequencyf_(sub)(k_(sub)), and decimates that signal to intermediate ratef_(dec)=M_(dec)f_(sym), where M_(dec) is a positive integer. Eachdecimated signal x_(dec)(n_(dec);k_(sub)) is then passed through asymbol-rate synchronous channelization operation (164 a)-(164 b)comprising a 1:M_(dec) serial-to-parallel converter and aM_(DoF)×M_(dec) channelization operator T_(DoF) (165), to formchannelized subband signalx_(DoF)(n_(sym);k_(sub))=T_(DoF)∘x_(sym)(n_(sym);k_(sub)) where

x_(sym)(n_(sym); k_(sub)) = [x_(dec)(M_(dec)n_(sym) + m_(dec); k_(sub))]_(m_(dec) = 0)^(M_(dec) − 1).The subband frequencies

{f_(sub)(k_(sub))}_(k_(sub) = 0)^(K_(sub) − 1)can be organized in accordance with Eqn (23); set to a preselected setof arbitrary frequencies; or adaptively determined based on channeldynamics or co-channel interference considerations.

Given the reception scenario described in FIG. 1 and FIG. 2 , and thereceived signal model given in Eqn (4)-Eqn (14), then the single-samplechannelizer output signal shown in FIG. 7 can be modeled by

$\begin{matrix}{{{x_{chn}\left( n_{sym} \right)} = {{i_{chn}\left( n_{sym} \right)} + {\sum\limits_{\ell = 1}^{L_{T}}{s_{chn}\left( {n_{sym};\ell} \right)}}}},} & {{Eqn}(25)}\end{matrix}$where i_(chn)(n_(sym))=T_(chn)∘i_(sym)(n_(sym)) ands_(chn)(n_(sym);l)=T_(chn)∘s_(sym)(n_(sym);l) are the K_(chn)×1interference and navigation signal l channelizer output signals,respectively, and where

${{i_{sym}\left( n_{sym} \right)} = {\left\lbrack {i_{R}\left( {T_{sym}\left( {n_{sym} + \frac{m_{ADC}}{M_{ADC}}} \right)} \right)} \right\rbrack{and}}}{{s_{sym}\left( {n_{sym};\ell} \right)} = \left\lbrack {s_{R}\left( {{T_{sym}\left( {n_{sym} + \frac{m_{ADC}}{M_{ADC}}} \right)};\ell} \right)} \right\rbrack}$are the M_(ADC)×1 interference and GNSS signal l S/P output vectors,respectively.

The '417 NPA, incorporated herein by reference, provides a detaileddescription of the signals obtaining at the output of asymbol-rate-synchronous channelizer with K_(chn)=M_(DoF). A simplerchannel model can be obtained using the polyphase filter aspect shown inFIG. 10 . In this case, under the simplifying assumption

$\begin{matrix}{{{s_{R}\left( {t;\ell} \right)} \approx {{g_{TR}(\ell)}e^{j2\pi{\alpha_{TR}(\ell)}t}{s_{T}\left( {{t - {\tau_{TR}(\ell)}};\ell} \right)}}},} & {{Eqn}(26)}\end{matrix}$i.e., ignoring affects of platform dynamics other than Doppler shiftcaused by the transmitter velocity observed at the receiver, then thechannelizer output signal s_(chn)(k_(chn),n_(sym);l) is given by

$\begin{matrix}{{{s_{chn}\left( {k_{chn},{n_{sym};\ell}} \right)} = {e^{j2\pi{\alpha_{TR}(\ell)}T_{sym}n_{sym}}{\sum\limits_{q_{sym}}{{a_{chn}\left( {k_{chn},{q_{sym};\ell}} \right)}{d_{T}\left( {{n_{sym} - q_{sym}};\ell} \right)}}}}},} & {{Eqn}(27)}\end{matrix}$where a_(chn)(k_(chn),q_(sym);l) is given by

$\begin{matrix}{{{a_{chn}\left( {k_{chn},{q_{sym};\ell}} \right)} = {e^{j2{\pi({{q_{sym}T_{sym}} - {\tau_{TR}(\ell)}})}{f_{chn}(k_{chn})}}e^{{- j}2\pi q_{sym}{\alpha_{TR}(\ell)}} \times {\int\limits_{- \infty}^{\infty}{{W_{chn}^{*}\left( e^{j2\pi{fT}_{ADC}} \right)}{H_{TR}\left( {f + {f_{chn}\left( k_{chn} \right)}} \right)}e^{j2{\pi({{q_{sym}T_{sym}} - {\tau_{TR}(\ell)}})}f}{df}}}}},} & {{Eqn}(28)}\end{matrix}$in which W(e^(j2πf)) is the discrete Fourier transform ofw_(chn)(m_(ADC)) and H_(TR)(f;l) is the frequency response of theend-to-end symbol shaping, given byH _(TR)(f;l)=g _(TR)(l)^(j2πα) ^(TR) ^((l)) H _(R)(f)H _(T)(f−α_(TR)(l);l)√{square root over (P _(T)(l))},  Eqn (29)where H_(T)(f;l) is the Fourier transform of h_(T)(t;l) given in Eqn (2)and H_(R)(f) is the frequency response of the receiver filteringoperations.

If H_(TR)(f;l) is bandlimited below f_(ADC)/2 e.g., using typicalpre-ADC antialiasing filters, the bandwidth of W(e^(j2πf)) is much lessthan the frequency variation in H_(TR)(f;l) and f_(chn)(k_(chn)) isgiven by Eqn (21), then Eqn (28) can be approximated bya _(chn)(k _(chn) ,q _(sym) ;l)≈a _(chn)(k _(chn) ;l)a _(sym)(q _(sym);l)  Eqn (30)where a_(chn)(k_(chn);l) and a_(sym)(q_(sym);l) are thefrequency-varying and time-varying components of the channel signature,

$\begin{matrix}{{{a_{chn}\left( {k_{chn};\ell} \right)} = {f_{ADC}{H_{TR}\left( {{f_{chn}\left( k_{chn} \right)};\ell} \right)}e^{{- j}2\pi{f_{chn}(k_{chn})}{\tau_{TR}(\ell)}}}},} & {{Eqn}(31)}\end{matrix}$ $\begin{matrix}{{{a_{sym}\left( {q_{sym};\ell} \right)} = {\left( {- 1} \right)^{{({K_{chn} - 1})}q_{sym}}{w_{sym}^{*}\left( {q_{sym} - {{\tau_{TR}(\ell)}f_{sym}}} \right)}e^{{- j}2\pi q_{sym}{\alpha_{TR}(\ell)}}}},} & {{Eqn}(32)}\end{matrix}$respectively, referred to herein as the channel frequency signature andchannel time signature, and where w_(sym)(τ) is the interpolatedchannelizer window, given by

$\begin{matrix}{{w_{sym}(\tau)} = {\sum\limits_{m_{ADC}}{{w_{chn}\left( m_{ADC} \right)}{{{Sa}\left( {\pi\left( {{\tau M_{ADC}} - m_{ADC}} \right)} \right)}.}}}} & {{Eqn}(33)}\end{matrix}$The channelized received signal s_(chn)(k_(chn),n_(sym);l) is thenapproximated bys _(chn)(k _(chn) ,n _(sym) ;l)≈a _(chn)(k _(chn) ;l)d _(R)(n _(sym);l),  Eqn (34)where d_(R)(n_(sym);l) is the signal l symbol sequence observed at thereceiver, given byd _(R)(n _(sym) ;l)=(a _(sym)(n _(sym) ;l)∘d _(T)(n _(sym) ;l))e ^(j2πα)^(TR) ^((l)T) ^(sym) ^(n) ^(sym) ,  Eqn (35)and where “∘” here denotes the convolution operation. Furtherdecomposing τ_(TR)(l) and α_(TR)(l) into symbol-normalized TOA and FOAcomponents

$\begin{matrix}{{\tau_{TR}(\ell)} = {\left( {{{\overset{\sim}{\tau}}_{TR}(\ell)} + {n_{TR}(\ell)}} \right)T_{sym}\left\{ {\begin{matrix}{\left. {{{\overset{\sim}{\tau}}_{TR}(\ell)} \in \left\lbrack \begin{matrix}0 & 1\end{matrix} \right.} \right),} & {{fractional}{fine}{TOA}} \\{{{n_{TR}(\ell)} \in {\mathbb{Z}}},} & {{TOA}{symbol}{offset}}\end{matrix},} \right.}} & {{Eqn}(36)}\end{matrix}$ $\begin{matrix}{{\alpha_{TR}(\ell)} = {\left( {{{\overset{\sim}{\alpha}}_{TR}(\ell)} + {k_{TR}(\ell)}} \right)f_{sym}\left\{ {\begin{matrix}{\left. {{\alpha_{TR}(\ell)} \in \left\lbrack \begin{matrix}{- \frac{1}{2}} & \frac{1}{2}\end{matrix} \right.} \right),} & {{fractional}{fine}{FOA}} \\{{{k_{TR}(\ell)} \in {\mathbb{Z}}},} & {{FOA}{Nyquist}{zone}}\end{matrix},} \right.}} & {{Eqn}(37)}\end{matrix}$respectively, then Eqn (34) can be replaced by

$\begin{matrix}{{{d_{R}\left( {n_{sym};\ell} \right)} = {\left( {{a_{sym}\left( {n_{sym};\ell} \right)} \circ {d_{T}\left( {{n_{sym} - {n_{TR}(\ell)}};\ell} \right)}} \right)e^{j2\pi{{\overset{\sim}{\alpha}}_{TR}(\ell)}n_{sym}}}},} & {{Eqn}(38)}\end{matrix}$ $\begin{matrix}{{{a_{sym}\left( {q_{sym};\ell} \right)} = {\left( {- 1} \right)^{{({K_{chn} - 1})}q_{sym}}{w_{sym}^{*}\left( {q_{sym} - {{\overset{\sim}{\tau}}_{TR}(\ell)}} \right)}e^{{- j}2\pi q_{sym}{\alpha_{TR}(\ell)}}}},} & {{Eqn}(39)}\end{matrix}$except for phase shift φ(l)=2π(f_(chn)(0)−{tilde over(α)}_(TR)(l))n_(TR)(l), which is subsumed into end-to-end link gain ing_(TR)(l) in Eqn (5). Then d_(R)(n_(sym);l) is completely characterizedby the channel time signature defined (over fine TOA ranging between 0and 1; the received TOA measured to integer number of symbols; and thefractional fine FOA ranging between −½ and ½.

For the GNSS signals listed in FIG. 4 , and assuming|α_(TR)(l)|<<f_(chp), then a_(chn)(k_(chn);l) can be furtherapproximated by

$\begin{matrix}{{{a_{chn}\left( {k_{chn};\ell} \right)} \approx {\frac{M_{ADC}}{\sqrt{M_{chp}}}{{Sa}\left( {\pi{f_{chn}\left( k_{chn} \right)}T_{chp}} \right)}{H_{R}\left( {f_{chn}\left( k_{chn} \right)} \right)}{g_{TR}(\ell)}\sqrt{P_{T}(\ell)}{\varepsilon_{R}\left( {k_{chn};\ell} \right)}}},} & {{Eqn}(40)}\end{matrix}$ $\begin{matrix}{{{\varepsilon_{R}\left( {k_{chn};\ell} \right)} = {\frac{1}{\sqrt{M_{chp}}}{C_{T}\left( {e^{{- j}2{\pi({{f_{chn}(k_{chn})} - {\alpha_{TR}(\ell)}})}T_{chp}};\ell} \right)}e^{{- j}2{\pi({{{f_{chn}(k_{chn})} - {\alpha_{TR}(\ell)}};\ell})}{\tau_{TR}(\ell)}}}},} & {{Eqn}(41)}\end{matrix}$where normalized observed ranging code frequency signatureε_(R)(k_(chn);l) captures the cross-channel frequency variability ofeach channel frequency signature due to the separate ranging code usedat each transmitter, and the differing TOA on each transmission path.For well-designed pseudo-random code sequences and M_(chp)>>1,ε_(R)(k_(chn);l) can be modeled as a zero-mean, unit-variance,independent and identically-distributed (i.i.d.) complex-Gaussian randomprocess. The channelized output signal can then be approximated by

$\begin{matrix}{{{x_{chn}\left( n_{sym} \right)} \approx {{i_{chn}\left( n_{sym} \right)} + {\sum\limits_{\ell = 1}^{L_{T}}{{a_{chn}(\ell)}{d_{R}\left( {n_{sym};\ell} \right)}}}}},} & {{Eqn}(42)}\end{matrix}$where

a_(chn)(ℓ) = [a_(chn)(k_(chn); ℓ)]_(k_(chn) = 0)^(K_(chn) − 1)is the K_(chn)×1 signal l channel frequency signature anda_(chn)(k_(chn);l) is given by Eqn (40)-Eqn (41) and d_(R)(n_(sym);l) isgiven by Eqn (38).

Assuming the background interference i_(R)(t) given in Eqn (4) iscomplex-Gaussian and stationary with power spectral density (PSD) S_(i)_(R) _(i) _(R) (f), then the interference power level in each channel isgiven by

$\begin{matrix}{{\left\langle {❘{i_{chn}\left( {k_{chn},n_{sym}} \right)}❘}^{2} \right\rangle = {\int\limits_{{- 1}/2}^{1/2}{{❘{W_{chn}\left( e^{j2\pi f} \right)}❘}^{2}{{\overset{\sim}{S}}_{i_{R}i_{R}}\left( {f + {{f_{chn}\left( k_{chn} \right)}T_{ADC}}} \right)}{df}}}},} & {{Eqn}(43)}\end{matrix}$where

${{\overset{\sim}{S}}_{i_{R}i_{R}}(f)} = {f_{ADC}{\sum\limits_{\ell}{{❘{H_{R}\left( {\left( {f + \ell} \right)f_{ADC}} \right)}❘}^{2}{S_{i_{R}i_{R}}\left( {\left( {f + \ell} \right)f_{ADC}} \right)}}}}$is the PSD of sampled interference signal i_(R)(T_(ADC)n_(ADC)).Assuming the ADC input signal is bandlimited to less than f_(ADC)/2ahead of the sampling operation, and that the PSD frequency variation islow over the passband of the polyphase filter frequency responseW_(chn)(e^(j2πf)), then Eqn (43) can be approximated by

$\begin{matrix}{\begin{matrix}{\left\langle {❘{i_{chn}\left( {k_{chn},n_{sym}} \right)}❘}^{2} \right\rangle \approx {f_{ADC}{❘{H_{R}\left( {f_{chn}\left( k_{chn} \right)} \right)}❘}^{2}S_{i_{R}i_{R}}\left( {f_{chn}\left( k_{chn} \right)} \right)\underset{{- 1}/2}{\overset{1/2}{\int}}{❘{W_{chn}\left( e^{j2\pi f} \right)}❘}^{2}{df}}} \\{= {f_{ADC}{❘{H_{R}\left( {f_{chn}\left( k_{chn} \right)} \right)}❘}^{2}{S_{i_{R}i_{R}}\left( {f_{chn}\left( k_{chn} \right)} \right)}{w_{chn}}_{2}^{2}}} \\{= {\frac{M_{ADC}^{2}}{M_{chp}}f_{chp}{❘{H_{R}\left( {f_{chn}\left( k_{chn} \right)} \right)}❘}^{2}{S_{i_{R}i_{R}}\left( {f_{chn}\left( k_{chn} \right)} \right)}}}\end{matrix},} & {{Eqn}(44)}\end{matrix}$where

${w_{chn}}_{2}^{2} = {\sum\limits_{m_{ADC}}{❘{w_{chn}\left( m_{ADC} \right)}❘}^{2}}$denotes the squared L2 Euclidean norm of the channelizer weights{w_(chn)(m_(ADC))} (158), and further assuming normalization constraint∥w_(chn)∥₂ ²=M_(ADC). More generally, the interference cross-correlationacross symbol lag and frequency channel offset can be approximated by

$\begin{matrix}{\begin{matrix}{{R_{i_{chn}i_{chn}}\left( {k_{chn},{\ell_{chn};m_{sym}}} \right)}\overset{\bigtriangleup}{=}\left\langle {{i_{chn}\left( {k_{chn},n_{sym}} \right)}{i_{chn}^{*}\left( {\ell_{chn},{n_{sym} - m_{sym}}} \right)}} \right\rangle} \\{\approx {\frac{M_{ADC}^{2}}{M_{chp}}f_{chp}{S_{i_{R}i_{R}}\left( \frac{{f_{chn}\left( k_{chn} \right)} + {f_{chn}\left( \ell_{chn} \right)}}{2} \right)}}} \\{\times \left( {- 1} \right)^{{({K_{chn} - 1})}m_{sym}}{\rho_{chn}\left( {{M_{ADC}m_{sym}},\frac{k_{chn} - \ell_{chn}}{M_{ADC}}} \right)}}\end{matrix},} & {{Eqn}(45)}\end{matrix}$where

${\rho_{chn}\left( {m,\alpha} \right)} = {\frac{1}{M_{ADC}}{\sum\limits_{n}{{w_{chn}(n)}{w_{chn}^{*}\left( {n - m} \right)}e^{{- j}2\pi\alpha n}}}}$is the discrete-time ambiguity function for channelizer window{w_(chn)(m_(ADC))} (158), normalized M_(ADC) so that |ρ_(chn)(m,α)|≤1.

FIG. 12 depicts the channel time signature (FIG. 12A) and normalizedambiguity function (FIG. 12B) induced by the polyphase-filter basedsymbol-rate synchronous channelizer (160) shown in FIG. 10 , usingsingle-symbol rectangularly-windowed channelizer weights (158). ThisFigure also obtains for the FFT-based symbol-rate synchronouschannelized shown in FIG. 8 and FIG. 9 . As shown in FIG. 12A, thechannel time signature is only substantive over a single symbol for fineTOA offsets between 0 and 1, and is nearly equal to unity within thisregion. The received symbol sequence d_(R)(n_(sym);l) given in Eqn (38)then simplifies to

$\begin{matrix}{{{d_{R}\left( {n_{sym};\ell} \right)} \approx {{d_{T}\left( {{n_{sym} - 1 - {n_{TR}(\ell)}};\ell} \right)}e^{j2\pi{{\overset{\sim}{\alpha}}_{TR}(\ell)}n_{sym}}}},} & {{Eqn}(46)}\end{matrix}$where the phase term −2π{tilde over (α)}_(TR)(l) is subsumed intog_(TR)(l). Similarly, the normalized ambiguity function shown in FIG.12B is equal to unity at zero channel and symbol offset. Hence thebackground interference for this channelizer window can be treated asindependent between channels and symbols, yielding K_(chn)×K_(chn)interference autocorrelation matrix (ACM)

$\begin{matrix}{R_{i_{chn}i_{chn}} = {\frac{M_{ADC}}{M_{chp}}f_{chp}{diag}{\left\{ {{❘{H_{R}\left( {f_{chn}\left( k_{chn} \right)} \right)}❘}^{2}{S_{i_{R}i_{R}}\left( {f_{chn}\left( k_{chn} \right)} \right)}} \right\}_{k_{chn} = 0}^{K_{chn} - 1}.}}} & {{Eqn}(47)}\end{matrix}$However, the channel model established above can be extended to anychannelizer window.

Multiplying x_(chn)(n_(sym)) by the inverse square-root of R_(i) _(chn)_(i) _(chn) yields normalized signal

$\begin{matrix}\begin{matrix}{{{{\overset{\sim}{x}}_{chn}\left( n_{sym} \right)} \approx {R_{i_{chn}i_{chn}}^{{- 1}/2}{x_{chn}\left( n_{sym} \right)}}},} \\{{\approx {{\varepsilon_{chn}\left( n_{sym} \right)} + {\sum\limits_{\ell = 1}^{L_{T}}{{u_{chn}(\ell)}{d_{R}\left( {n_{sym};\ell} \right)}}}}},}\end{matrix} & {{Eqn}(48)}\end{matrix}$where d_(R)(n_(sym);l) is given by Eqn (46), ε_(chn)(n_(sym)) is aK_(chn)×1 i.i.d. complex-Gaussian random process with zero mean and ACMI_(K) _(chn) , and U_(chn)(l) is the K_(chn)×1 signal l normalizedchannel frequency signature given by

$\begin{matrix}{{u_{chn}(\ell)} = {\left\lbrack {\frac{{Sa}\left( {\pi{f_{chn}\left( k_{chn} \right)}T_{chp}} \right)}{\sqrt{f_{chp}{S_{i_{R}i_{R}}\left( {f_{chn}\left( k_{chn} \right)} \right)}}}{\varepsilon_{R}\left( {k_{chn};\ell} \right)}} \right\rbrack{g_{TR}(\ell)}{\sqrt{P_{T}(\ell)}.}}} & {{Eqn}(49)}\end{matrix}$In theory, a set of K_(chn)×1 combining weights {tilde over(w)}_(max-SINR)(l) can then be developed that extracts d_(R)(n_(sym);l)from {tilde over (x)}_(chn)(n_(sym)) with maximum-attainablesignal-to-interference-and-noise ratio (max-SINR). For the channel modelgiven in Eqn (48)-Eqn (49), and assuming the navigation symbol sequencesare independent for each transmitter, {tilde over (w)}_(max-SINR)(l) isgiven by

$\begin{matrix}{\begin{matrix}{{w_{max - {SINR}}(\ell)} \propto {\left( {I_{K_{chn}} + {{U_{chn}\left( {\sim\ell} \right)}{U_{chn}^{H}\left( {\sim\ell} \right)}}} \right)^{- 1}{u_{chn}(\ell)}}} \\{= {\left( {I_{K_{chn}} - {{U_{chn}\left( {\sim\ell} \right)}\left( {I_{L_{T} - 1} + {U_{chn}^{H}\left( {\sim\ell} \right){U_{chn}\left( {\sim\ell} \right)}}} \right)^{- 1}U_{chn}^{H}}} \right){u_{chn}(\ell)}}}\end{matrix},} & {{Eqn}(50)}\end{matrix}$where U_(chn)(˜l)=[u_(chn)(l′)]_(l′≠l) is the K_(chn)×(L_(T)−1) matrixof normalized frequency signatures interfering with signal l, and themax-SINR for symbol sequence l is given by

$\begin{matrix}{\begin{matrix}{{\gamma_{max - {SINR}}(\ell)} \approx {{u_{chn}(\ell)}}_{2}^{2}} \\{{- {u_{chn}^{H}(\ell)}}{U_{chn}\left( {\sim\ell} \right)}\left( {I_{L_{T} - 1} + {U_{chn}^{H}\left( {\sim\ell} \right){U_{chn}\left( {\sim\ell} \right)}}} \right)^{- 1}{U_{chn}^{H}\left( {\sim\ell} \right)}{u_{chn}(\ell)}}\end{matrix}.} & {{Eqn}(51)}\end{matrix}$Modeling ε_(R)(k_(sub);l) as i.i.d. complex Gaussian with zero mean andunity variance, appropriate for unknown, well-modeled long rangingcodes, then Eqn (51) has mean lower bound

$\begin{matrix}{\begin{matrix}{{{\overset{\_}{\gamma}}_{max - {SINR}}(\ell)} = {E\left\{ {\gamma_{max - {SINR}}(\ell)} \right\}}} \\{\geq \left( {{{\overset{\_}{\gamma}}_{max - {SNR}}(\ell)} - {\left( {L_{T} - 1} \right)\left( \frac{{\overset{\_}{\gamma}}_{max - {INR}}(\ell)}{1 + {{\overset{\_}{\gamma}}_{max - {INR}}(\ell)}} \right)\underset{k_{chn}}{\max}{{\overset{\_}{\gamma}}_{{Rx} - {SNR}}\left( {k_{chn};\ell} \right)}}} \right.}\end{matrix},} & {{Eqn}(52)}\end{matrix}$ $\begin{matrix}{\rightarrow\left\{ {\begin{matrix}{{{\overset{\_}{\gamma}}_{max - {SNR}}(\ell)},} & {{{\overset{\_}{\gamma}}_{max - {INR}}(\ell)}{1}} \\{\left( {{{\overset{\_}{\gamma}}_{max - {SNR}}(\ell)} - {\left( {L_{T} - 1} \right)\max\limits_{k_{chn}}{\overset{\_}{\gamma}}_{max - {SNR}}\left( {k_{chn};\ell} \right)}} \right),} & {{{{\overset{\_}{\gamma}}_{max - {INR}}(\ell)}}1}\end{matrix},} \right.} & {{Eqn}(53)}\end{matrix}$where γ _(Rx-SNR)(k_(chn) ^(;l) and γ) _(max-SNR)(l) are the meanreceive SNR (Rx-SNR) and maximum-attainable SNR (max-SNR) of signal l inthe absence of interference navigation signals, respectively,

$\begin{matrix}{\begin{matrix}{{{\overset{\_}{\gamma}}_{{Rx} - {SNR}}\left( {k_{chn};\ell} \right)} = {E\left\{ {❘{u_{chn}\left( {k_{chn};\ell} \right)}❘} \right\}}} \\{= {\frac{{Sa}^{2}\left( {\pi{f_{chn}\left( k_{chn} \right)}T_{chp}} \right)}{f_{chp}{S_{i_{R}i_{R}}\left( {f_{chn}\left( k_{chn} \right)} \right)}}{❘{g_{TR}(\ell)}❘}^{2}{P_{T}(\ell)}}}\end{matrix},} & {{Eqn}(54)}\end{matrix}$ $\begin{matrix}{\begin{matrix}{{{\overset{\_}{\gamma}}_{max - {SNR}}(\ell)} = {E\left\{ {{u_{chn}(\ell)}}_{2}^{2} \right\}}} \\{= {\sum\limits_{k_{chn} = 0}^{K_{chn} - 1}{{\overset{\_}{\gamma}}_{{Rx} - {SNR}}\left( {k_{chn};\ell} \right)}}}\end{matrix},} & {{Eqn}(55)}\end{matrix}$and where γ _(max-INR)(l) is the mean max-attainable SNR of navigationsignals interfering with signal l,

$\begin{matrix}{{{\overset{\_}{\gamma}}_{max - {INR}}(\ell)} = {\frac{1}{L_{T} - 1}{\sum\limits_{\ell^{\prime} \neq \ell}{{{\overset{\_}{\gamma}}_{max - {SNR}}\left( \ell^{\prime} \right)}.}}}} & {{Eqn}(56)}\end{matrix}$As Eqn (53) shows, at high receive SNR, the max-SINR combiner usesL_(T)−1 combiner degrees of freedom (DoF's) to excise the navigationsignals impinging on the receiver, and employs the remainingK_(chn)−L_(T)+1 combiner DoF's to suppress the background interferencei_(chn)(n_(sym)).

As disclosed in the '417 NPA, incorporated herein by reference, linearalgebraic methods to determine max-SINR weights can be devised giveneither knowledge of the content of {d_(T)(n_(sym);l)}_(l=1) ^(L) ^(T) ,e.g., provided by third-party sources; knowledge of a component of{d_(T)(n_(sym);l)}_(l=1) ^(L) ^(T) , e.g., a known/periodic pilotsignal; or knowledge of some other exploitable structure of{d_(T)(n_(sym);l)}_(l=1) ^(L) ^(T) , as listed in FIG. 4 . These methodscan be used to detect the navigation signals in the environment,estimate the max-SINR of the combiner output symbol sequences for thosesignals, and determine at least the geo-observables {n_(TR)(l),{tildeover (α)}_(TR)(l)}_(l=1) ^(L) ^(T) for those signals, and if neededestimate information-bearing components of the transmitted symbolstreams {d_(T)(n_(sym);l)}_(l=1) ^(L) ^(T) . Moreover, these techniquescan perform these operations without prior knowledge of the signalranging code or receive frequency signature for the signals, or a searchover TOA and FOA is the ranging code is known.

However, as also disclosed in the '417 NPA, linear-algebraic methodsthat can develop combiner weights covering the entire navigation signalpassband, e.g., K_(chn) ˜1,000 for the GPS L1 legacy signal, and K_(chn)˜10,000 for the GPS L5 civil signal, require O(K_(chn) ²)operations/symbol to be implemented. Moreover, they require O(K_(chn))symbols to converge to a useful solution, e.g., 2-to-4 seconds for theGPS L1 legacy signal, and 20-40 seconds for the GPS L5 civil signal.This convergence time introduces additional complexity in GNSS receptionscenarios, due to channel dynamics caused by movement of the GNSSsatellite vehicles.

In the '417 NPA, partial subband methods that reduce K_(chn) to amanageable value are disclosed to overcome these issues. These methodscan provide strong advantage in the presence of strong MOS-DSSS spoofingand jamming signals. However, they sacrifice substantive processing gainto achieve this capability at reasonable complexity and over shortreception intervals. This issue can be especially significant for modernwideband navigation signals such as the GPS L5 civil signal. Themulti-subband approach provides a path to overcome this limitation.

Returning to FIG. 10 , reshape operation (161) shown in FIG. 10separates x_(chn)(n_(sym)) into K_(sub) subbands, each comprisingM_(DoF) frequency channels such that K_(chn)=K_(sub)M_(DoF), and thesignal in each subband can be represented by

$\begin{matrix}{\begin{matrix}{{x_{DoF}\left( {n_{sym};k_{sub}} \right)} = \begin{pmatrix}{x_{chn}\left( {{M_{DoF}k_{sub}},n_{sym}} \right)} \\ \vdots \\{x_{chn}\left( {{{M_{DoF}k_{sub}} + M_{DoF} - 1},n_{sym}} \right)}\end{pmatrix}} \\{\approx {{i_{DoF}\left( {n_{sym};k_{sub}} \right)} + {\sum\limits_{\ell = 1}^{L_{T}}{{a_{DoF}\left( {k_{sub};\ell} \right)}{d_{R}\left( {n_{sym};\ell} \right)}}}}}\end{matrix},} & {{Eqn}(57)}\end{matrix}$where d_(R)(n_(sym);l), given by Eqn (46) for the rectangularly-windowedchannelizer, is shared for all subbands, and a_(DoF)(k_(sub);l) is theM_(DoF)×1 signal l frequency signature for subband k_(sub),

$\begin{matrix}{{{a_{DoF}\left( {k_{sub};\ell} \right)} = \begin{pmatrix}{a_{chn}\left( {{M_{DoF}k_{sub}},\ell} \right)} \\ \vdots \\{a_{chn}\left( {{{M_{DoF}k_{sub}} + M_{DoF} - 1},\ell} \right)}\end{pmatrix}},} & {{Eqn}(58)}\end{matrix}$and where i_(DoF)(n_(sym);k_(sub)) is the background noise andinterference received in subband k_(sub). If i_(R)(t) is stationary withPSD S_(i) _(R) _(i) _(R) (f) at the LPF output, then the zero-lag ACM ofi_(DoF)(n_(sym);k_(sub)) is further approximated by

$\begin{matrix}{{{R_{i_{DoF}i_{DoF}}\left( k_{sub} \right)} \approx {\frac{M_{ADC}^{2}}{M_{chp}}f_{chp}{❘{H_{R}\left( {f_{sub}\left( k_{sub} \right)} \right)}❘}^{2}{S_{i_{R}i_{R}}\left( {f_{sub}\left( k_{sub} \right)} \right)}P_{sub}}},} & {{Eqn}(59)}\end{matrix}$where

${f_{sub}\left( k_{sub} \right)} = {\left( {k_{sub} - \frac{K_{sub} - 1}{2}} \right)M_{DoF}f_{sym}i}$is the center frequency of subband k_(sub), and where

$P_{sub} = \left\lbrack {\frac{1}{M_{ADC}}{\sum\limits_{m}{{❘{w_{chn}(m)}❘}^{2}e^{{- j}2{\pi({k - \ell})}m/M_{ADC}}}}} \right\rbrack_{k,{\ell = 0}}^{M_{DoF} - 1}$is the normalized subband interference ACM, which is equal to I_(M)_(DoF) for the single-symbol rectangular channelizer window.

If M_(DoF)≥L_(T), then navigation symbol sequences l can be received ineach subband using an appropriately designed set of max-SINR linearin-subband linear combining weights w_(max-SINR)(k_(sub);l), such thatcombiner output symbol sequence {circumflex over(d)}_(R)(n_(sym);k_(sub);l)=w_(max-SINR)^(H)(k_(sub);l)x_(sub)(n_(sym);k_(sub)) excises the interferingnavigation signals {d_(R)(n_(sym);l′)}_(l′≠l) also received in thesubband using L_(T)−1 degrees of freedom, and suppresses the backgroundinterference i_(sub)(n_(sym);k_(chn)) in the subband using the remainingM_(DoF)−L_(T)+1 degrees of freedom, and where (⋅)^(H) denotes theHermitian transpose operation. Assuming a nearly-flat signature andinterference response over each subband, and rectangular channelizerwindows, then the SINR achievable using this linear combiner satisfiesmean lower bound

$\begin{matrix}{{{{\overset{\_}{\gamma}}_{max - {SINR}}\left( {k_{sub};\ell} \right)} \geq {\left( {M_{DoF} - {\left( {L_{T} - 1} \right)\left( \frac{{\overset{\_}{\gamma}}_{max - {INR}}\left( {k_{sub};\ell} \right)}{1 + {{\overset{\_}{\gamma}}_{max - {INR}}\left( {k_{sub};\ell} \right)}} \right)}} \right){{\overset{\_}{\gamma}}_{{Rx} - {SNR}}\left( {k_{sub};\ell} \right)}}},} & {{Eqn}(60)}\end{matrix}$ $\begin{matrix}{\rightarrow\left\{ \begin{matrix}{{M_{DoF}{{\overset{\_}{\gamma}}_{{Rx} - {SNR}}\left( {k_{sub};\ell} \right)}},} & {{{\overset{\_}{\gamma}}_{max - {INR}}\left( {k_{sub};\ell} \right)}{1}} \\{{\left( {M_{DoF} - L_{T} + 1} \right){{\overset{\_}{\gamma}}_{{Rx} - {SNR}}\left( {k_{sub};\ell} \right)}},} & {{{{\overset{\_}{\gamma}}_{max - {INR}}\left( {k_{sub};\ell} \right)}}1}\end{matrix} \right.} & {{Eqn}(61)}\end{matrix}$in each subband, where γ _(Rx-SNR)(k_(sub);l) and γ_(max-INR)(k_(sub);l) are the mean receive signal l SNR and themax-attainable navigation signal interference received along with thatsignal in subband k_(sub), respectively

$\begin{matrix}{{{{\overset{\_}{\gamma}}_{{Rx} - {SNR}}\left( {k_{sub};\ell} \right)} \approx {\frac{{Sa}^{2}\left( {\pi{f_{sub}\left( k_{sub} \right)}T_{chp}} \right)}{f_{chp}{S_{i_{R}i_{R}}\left( {f_{sub}\left( k_{sub} \right)} \right)}}{❘{g_{TR}(\ell)}❘}^{2}{P_{T}(\ell)}}},} & {{Eqn}(62)}\end{matrix}$ $\begin{matrix}{{{\overset{\_}{\gamma}}_{max - {INR}}\left( {k_{sub};\ell} \right)} \approx {\frac{M_{DoF}}{L_{T} - 1}{\sum\limits_{\ell^{\prime} \neq \ell}{{{\overset{\_}{\gamma}}_{{Rx} - {SNR}}\left( {k_{sub};\ell^{\prime}} \right)}.}}}} & {{Eqn}(63)}\end{matrix}$As Eqn (61) shows, the max-SINR weights can excise up to L_(T)−1 strongMOS-DSSS signals impinging on the receiver in each subband, and canprovide an additional factor of M_(DoF)−L_(T)+1 SNR gain to suppress theremaining background noise and interference in each subband. In low-SNRenvironments where all of the navigation signals are received well belowthe noise floor (γ _(RX-SNR)(k_(sub);l)<<1/M_(DoF)), the max-SINRweights can provide the full factor-of-M_(DoF) SNR gain available to thereceiver.

In aspects of the invention, the symbol sequence estimates from eachsubband are then further combined using cross-band linear combiningweights

{g_(sub)(k_(sub); ℓ)}_(k_(sub) = 0)^(K_(sub) − 1),yielding multi-subband symbol sequence estimate

$\begin{matrix}{\begin{matrix}{{{\hat{d}}_{R}\left( {n_{sym};\ell} \right)} \approx {\sum\limits_{k_{sub} = 0}^{K_{sub} - 1}{{g_{sub}^{*}\left( {k_{sub};\ell} \right)}{{\hat{d}}_{R}\left( {n_{sym};k_{sub};\ell} \right)}}}} \\{\approx {{g_{sub}^{H}(\ell)}{{\hat{d}}_{sub}\left( {n_{sym};\ell} \right)}}}\end{matrix}.} & {{Eqn}(64)}\end{matrix}$Assuming each subband has substantively excised the MOS-DSSS signalsimpinging on the receiver, and has provided a unit-power output signal,then {circumflex over (d)}_(sub)(n_(sym);l) can be approximated by

$\begin{matrix}{{{\hat{d}}_{R}\left( {n_{sym};\ell} \right)} \approx {{\sum_{max - {SINR}}^{1/2}{(\ell){\varepsilon\left( {n_{sym};\ell} \right)}}} + {{a_{max - {SINR}}(\ell)}{{\hat{d}}_{R}\left( {n_{sym};\ell} \right)}}}} \\{{\sum_{max - {SINR}}(\ell)} = {{diag}\left\{ \frac{\gamma_{max - {SINR}}\left( {k_{sub};\ell} \right)}{\left( {1 + {\gamma_{max - {SINR}}\left( {k_{sub};\ell} \right)}} \right)^{2}} \right\}}} \\{{a_{max - {SINR}}(\ell)} = \left\lbrack \frac{\gamma_{max - {SINR}}\left( {k_{sub};\ell} \right)}{1 + {\gamma_{max - {SINR}}\left( {k_{sub};\ell} \right)}} \right\rbrack}\end{matrix}.$The SINR of this signal is maximized by settingg_(sub)(l)=[1+γ_(Max-SINR)(k_(sub);l)], yielding output SINR

$\begin{matrix}{{{\gamma_{max - {SINR}}\left( {n_{sym};\ell} \right)} = {\sum\limits_{k_{sub} = 0}^{K_{sub} - 1}{\gamma_{max - {SINR}}\left( {k_{sub};\ell} \right)}}},} & {{Eqn}(65)}\end{matrix}$which has mean lower bound

$\begin{matrix}{{{{\overset{\_}{\gamma}}_{max - {SINR}}(\ell)} \geq {\sum\limits_{k_{sub} = 0}^{K_{sub} - 1}{\left( {M_{DoF} - {\left( {L_{T} - 1} \right)\left( \frac{{\overset{\_}{\gamma}}_{max - {INR}}\left( {k_{sub};\ell} \right)}{1 + {{\overset{\_}{\gamma}}_{max - {INR}}\left( {k_{sub};\ell} \right)}} \right)}} \right){{\overset{\_}{\gamma}}_{{Rx} - {SNR}}\left( {k_{sub};\ell} \right)}}}},} & {{Eqn}(66)}\end{matrix}$ $\begin{matrix}{\rightarrow\left\{ {\begin{matrix}{{M_{DoF}{\sum\limits_{k_{sub}}{{\overset{\_}{\gamma}}_{{Rx} - {SNR}}\left( {k_{sub};\ell} \right)}}},} & {{{\overset{\_}{\gamma}}_{max - {INR}}\left( {k_{sub};\ell} \right)}{1}} \\{{\left( {M_{DoF} - L_{T} + 1} \right){\sum\limits_{k_{sub}}{{\overset{\_}{\gamma}}_{{Rx} - {SNR}}\left( {k_{sub};\ell} \right)}}},} & {{{{\overset{\_}{\gamma}}_{max - {INR}}\left( {k_{sub};\ell} \right)}}1}\end{matrix}.} \right.} & {{Eqn}(67)}\end{matrix}$Thus, the multi-subband solution can recover all or most of theprocessing gain of the full-channelizer max-SINR combiner, if M_(DoF) isgreater than the expected number of MOS-DSSS signals impinging on thereceiver.

In-subband linear combining weights approaching the max-SINR solutioncan be computed using linear-algebraic methods disclosed in the '417NPA, given either knowledge of the content of {d_(T)(n_(sym);l)}_(l=1)^(L) ^(T) , e.g., provided by third-party sources; knowledge of acomponent of {d_(T)(n_(sym);l)}_(l=1) ^(L) ^(T) , e.g., a known/periodicpilot signal; or other exploitable structure of {d_(T)(n_(sym);l)}_(l=1)^(L) ^(T) , as listed in FIG. 4 . These methods also can be used toestimate the max-SINR obtaining in each subband, thereby providingcross-subband weights for the second combining stage shown in Eqn (64).The multi-subband solution can further be used to estimate the fullmax-SINR of the received symbol sequences, detect the navigation signalsin the environment, determine at least the geo-observables{n_(TR)(l),{tilde over (α)}_(TR)l)}_(l=1) ^(L) ^(T) for those signals,and if needed estimate information-bearing components of the transmittedsymbol streams {d_(T)(n_(sym);l)}_(l=1) ^(L) ^(T) . Moreover, thesetechniques can perform these operations without prior knowledge of thesignal ranging code or receive frequency signature for the signals, or asearch over TOA and FOA is the ranging code is known.

In contrast to the full-band solution, however, the complexity of themulti-subband method scales quadratically with M_(DoF) and linearly withK_(sub), such that the full set of K_(chn) channels provided by thesymbol-rate synchronous channelizer can be processing at a complexity ofO(K_(sub)M_(DoF) ²)=O(K_(chn)M_(DoF)) operations/symbol—a factor ofK_(sub) saving in operations relative to the full-band system. Moreover,the number of symbols needed to provide a stable solution using themethods disclosed in the '417 NPA are O(M_(DoF)), also a factor ofK_(sub) reduction in convergence time relative to the full-band methods.In the invention, the value of M_(DoF) becomes a design parameterdictated by the number of MOS-DSSS signals expected to be encountered inthe receive environment, and the desired complexity and convergence timeof the signal reception algorithms, independent from the bandwidth ofthe receiver.

As an specific example, setting K_(chn)=960 for the GPS L1 legacy signaland K_(chn)=9,600 for the GPS L5 civil signal, i.e., and settingM_(DoF)=60 in both cases to allow reception of all of the GPS signals inthe field of view of the receiver as well as 30-45 beacons or spoofers,then the multi-subband processor has a complexity and convergence timereduction of 16 for the GPS L1 legacy signal, and 160 for the GPS L5civil signal, allowing convergence in as little as 120 ms for bothmethods and complexity of O(57.6) Mops/s for the GPS L1 legacy signaland O(576) Mops/s for the GPS L5 civil signal—well within thecapabilities of modern DSP equipment, and low-cost DSP for the GPS L1legacy signal. Moreover, the multi-subband approach is highly amenableto parallel processing methods, facilitating it's implementation inFPGA's and general-purpose GPU (GPGPU) architectures.

Taking channel time-variation given in Eqn (5)-Eqn (14) due to movingtransmitters and/or receivers more precisely into account, then overreception intervals on the order of 0-to-2 seconds, Eqn (42) generalizesto

$\begin{matrix}{{{x_{chn}\left( n_{sym} \right)} \approx {{i_{chn}\left( n_{sym} \right)} + {\sum\limits_{\ell = 1}^{L_{T}}{{a_{chn}\left( {n_{sym};\ell} \right)}{d_{R}\left( {n_{sym};\ell} \right)}}}}},} & {{Eqn}(68)}\end{matrix}$where time-varying frequency-signature a_(chn)(n_(sym);l) isapproximated by

$\begin{matrix}{{{a_{chn}\left( {n_{sym};\ell} \right)} \approx {{a_{chn}(\ell)} \odot \left\lbrack e^{{- j}2{\pi({{f_{chn}(k_{chn})} - {\alpha_{TR}(\ell)}})}{T_{sym}({{{\overset{\sim}{\tau}}_{TR}(\ell)} + {{\tau_{TR}^{(1)}(\ell)}n_{sym}}})}} \right\rbrack}},} & {{Eqn}(69)}\end{matrix}$and the observed symbol sequence is given by

$\begin{matrix}{\begin{matrix}{{d_{R}\left( {n_{sym};\ell} \right)} \approx \begin{matrix}\left( {a_{sym}{\left( {n_{sym};\ell} \right) \otimes}} \right. \\{\left. {d_{T}\left( {{n_{sym} - {n_{TR}(\ell)}};\ell} \right)} \right)e^{j2{\pi({{{{\overset{\sim}{\alpha}}_{TR}(\ell)}n_{sym}} + {\frac{1}{2}{{\overset{\sim}{\alpha}}_{TR}^{(1)}(\ell)}n_{sym}^{2}}})}}}\end{matrix}} \\\left. \rightarrow{}{{d_{T}\left( {{n_{sym} - {n_{TR}(\ell)} - 1};\ell} \right)}e^{j2{\pi({{{{\overset{\sim}{\alpha}}_{TR}(\ell)}n_{sym}} + {\frac{1}{2}{{\overset{\sim}{\alpha}}_{TR}^{(1)}(\ell)}n_{sym}^{2}}})}}} \right.\end{matrix},} & {{Eqn}(70)}\end{matrix}$and where “⊙” denotes the element-wise multiplication (Hadamard product)operation, τ_(TR) ⁽¹⁾(l) is the observed differential TOA (DTOA) givenin Eqn (10), and {acute over (α)}_(TR) ⁽¹⁾(l)=α_(TR) ⁽¹⁾(l)T_(sym) ² isthe symbol-normalized observed differential FOA (DFOA). Hence the DTOAprincipally affects the channel frequency signature, by inducing alinear frequency shift across the symbol-rate synchronous frequencychannels, while the DFOA principally affects the channel time signature,by inducing a quadratic frequency shift over the time symbols. However,it should be noted that the FOA is linearly related to the DTOA, asshown in Eqn (9), hence it affects both signature components.

For typical GNSS reception scenarios, τ_(TR) ⁽¹⁾(l) is typically lessthan 4 μs/s in magnitude, resulting in a link FOA of ±6.3 kHz at the L1GPS center frequency, and ±4.7 kHz at the GPS L5 center frequency. FromEqn (69), This DTOA value can also cause a differential frequency shiftof as much as 8 Hz over the ±1.023 MHz L1 GPS legacy signal band, or 80Hz over the ±10.23 MHz L5 civil GPS band; hence it must be taken intoaccount in any geo-observable estimation algorithm implemented over >10ms reception intervals.

In this regard, the multi-subband approach shown in FIG. 10 provides anadditional benefit, by separating the frequency channels into narrowsubbands during the reshape operation (161). In this case, the subbandsignal can be modeled by

$\begin{matrix}{{{x_{DoF}\left( n_{sym} \right)} \approx {{i_{DoF}\left( n_{sym} \right)} + {\sum\limits_{\ell = 1}^{L_{T}}{{a_{DoF}\left( {n_{sym};\ell} \right)}{d_{R}\left( {n_{sym};k_{sub};\ell} \right)}}}}},} & {{Eqn}(71)}\end{matrix}$ $\begin{matrix}{{d_{R}\left( {n_{sym};k_{sub};\ell} \right)} =} & {{Eqn}(72)}\end{matrix}$${{d_{T}\left( {{n_{sym} - {n_{TR}(\ell)} - 1};\ell} \right)}e^{{- j}2{\pi({f_{T} + {f_{sub}(k_{sub})}})}{T_{sym}({{{\tau_{TR}^{(1)}(\ell)}n_{sym}} + {\frac{1}{2}{{\overset{\sim}{\tau}}_{TR}^{(2)}(\ell)}n_{sym}^{2}}})}}},$$\begin{matrix}{{a_{DoF}\left( {n_{sym};\ell} \right)} = {{{a_{DoF}(\ell)} \odot \left\lbrack e^{{- j}2{\pi({m_{DoF} - {(\frac{M_{DoF} - 1}{2})} - {{\alpha_{TR}(\ell)}T_{sym}}})}{({{{\overset{\sim}{\tau}}_{TR}(\ell)} + {{\tau_{TR}^{(1)}(\ell)}n_{sym}}})}} \right\rbrack}.}} & {{Eqn}(73)}\end{matrix}$In aspects of the invention described herein, the substantivecross-subband frequency shift modeled in Eqn (72) is estimated as partof the geo-observable estimation procedure. The observedtime-variability in the subband frequency signature a_(DoF)(n_(sym);l)modeled in Eqn (73) induces a much lower in-subband frequency shift, dueto the much lower bandwidth of the subband. For the example cited above,where M_(DoF)=60, a DTOA of 4 μs/s induces a frequency shift of 0.24 Hzacross the subband, or 0.12 cycles over 500 ms. As disclosed in the '417NPA, this frequency shift creates low-level dispersive components thatcan be excised as part of the adaptation process for sufficiently largevalues of M_(DoF); the value considered here is likely to be more thansufficient for typical GNSS reception scenarios, even in the presence ofstrong ground beacons, and in the presence of strong spoofers attemptingto emulate GNSS transmitter dynamics.

Similarly, for typical GNSS reception scenarios, α_(TR) ⁽¹⁾(l) istypically less than 3 Hz/s in magnitude. As a consequence, its affect isminimal for reception intervals of 500 ms or less, and manageable forreception intervals on the order of 2 seconds or less, using aspects ofthe invention disclosed herein.

Accounting for worst-case channel dispersion, if M_(DoF)≥2L_(T) theentire network symbol stream can be extracted from the channel, i.e.,the interfering MOS-DSSS symbol sequences can be excised from each GNSSsymbol, using purely linear combining operations, and even if thenavigation signals are received with high-SNR inducing significantcross-interference. This can include methods well known to the signalprocessing community, e.g., blind adaptive baseband extraction methodsdescribed in the prior art, and linear minimum-mean-square-error (LMMSE)methods described in the prior art. For signals transmitted from MEOGNSS SV's, and in the absence of pseudolites or spoofers operating inthe same band as those SV's, no more than 12 SV's are likely to bewithin the field of view of a GNSS receiver at any one time (L_(T)≤12).Over short observation intervals, maximum substantive rank changeinduced by the MOS-DSSS signals is therefore likely to be 24. Thisnumber can grow to 48 in the presence of 12 spoofers “assigned” to eachlegitimate navigation signal. In both cases, this is much less than thenumber of channels available for any GNSS signals listed in FIG. 4 .

This channel response is also exactly analogous to channel responsesinduced in massive MIMO networks currently under investigation fornext-generation (5G) cellular communication systems. However, itachieves this response using only a single-feed receiver front-end,thereby bypassing the most challenging aspect of massive MIMOtransceiver technology. And it provides an output signal with aneffective data rate of 1 ksps for all of the signals listed in FIG. 4 ,as opposed to 10-20 Msps for massive MIMO networks under considerationfor 5G cellular communication applications. This receiver front-end alsoprovides considerable flexibility in the number of degrees of freedomM_(DoF) used at the receiver, e.g., by modifying the ADC sampling rate,or the number of FFT bins used in the channelizer, or any combinationthereof (albeit, at loss in processing gain if the channelizer does notfully cover the GNSS signal passband).

Lastly, the digital signal processing (DSP) operations needed to exploitthis channel response are expected to be very similar to operationsneeded for 5G data reception, albeit at a 3-4 order-of-magnitude lowerswitching rate. Given the massive investment expected in 5Gcommunications over the next decade, and the ongoing exponentialimprovements in cost and performance of DSP processing and memory, e.g.,Moore's and Kryder's Laws, the ability to fully exploit this channelresponse will become increasingly easier over time.

The previous description is provided to enable any person skilled in theart to practice the various aspects described herein. Variousmodifications to these aspects will be readily apparent to those skilledin the art, and the generic principles defined herein may be applied toother aspects. Thus, the claims are not intended to be limited to theaspects shown herein, but is to be accorded the full scope consistentwith the language claims, wherein reference to an element in thesingular is not intended to mean “one and only one” unless specificallyso stated, but rather “one or more.” The word “exemplary” is used hereinto mean “serving as an example, instance, or illustration.” Any aspectdescribed herein as “exemplary” is not necessarily to be construed aspreferred or advantageous over other aspects. Unless specifically statedotherwise, the term “some” refers to one or more. The phrase “A or B”may correspond to A only, B only, or A and B. Combinations such as “atleast one of A, B, or C,” “one or more of A, B, or C,” “at least one ofA, B, and C,” “one or more of A, B, and C,” and “A, B, C, or anycombination thereof” include any combination of A, B, and/or C, and mayinclude multiples of A, multiples of B, or multiples of C. Specifically,combinations such as “at least one of A, B, or C,” “one or more of A, B,or C,” “at least one of A, B, and C,” “one or more of A, B, and C,” and“A, B, C, or any combination thereof” may be A only, B only, C only, Aand B, A and C, B and C, or A and B and C, where any such combinationsmay contain one or more member or members of A, B, or C. The words“module,” “block,” “element,” “device,” and the like may not be asubstitute for the word “means.” As such, no claim element is to beconstrued as a means plus function unless the element is expresslyrecited using the phrase “means for.”

Extension to Multifeed Reception

FIG. 13 depicts aspects of the invention, in which the MOS-DSSSnavigation signals are received over M_(feed) feeds using a set ofspatial and/or polarization diverse antennas (90 a-90 c). In someaspects, that antennas are additionally coupled from a larger set ofantennas to M_(feed) feeds using a beamforming network (BFN) (94), e.g.,a Butler mode former, to provide spatial beamsteering operations,exclude known interference sources, or extract stronger and/or spatiallywhitened modes from the antenna array. The M_(feed) feeds are thencoherently converted to complex-baseband using a direct-conversionreceiver bank (200), to form M_(feed)×1 signal vector

x_(R)(t) = [x_(R)(t; m_(feed))]_(m_(feed) = 1)^(M_(feed)).The feed vector x_(R)(t) is then sampled by a bank of dual-ADC's (243),at sampling rate M_(ADC)f_(sym) determined by a common clock (117) wheref_(sym) is the baseband symbol rate of the MOS-DSSS navigation signalstransmitted to the receiver, and M_(ADC) is a positive integer.

Assuming coherent downconversion of the received signals, the complexM_(feed)×1 signal generated output from the receiver bank (200) ismodeled as

${{x_{R}(t)} = {{i_{R}(t)} + {\sum\limits_{\ell = 1}^{L}{s_{R}\left( {t;\ell} \right)}}}},$where i_(R)(t) comprises the M_(feed)×1 vector of background noise andco-channel interference (CCI) present in the receiver passband, ands_(R)(t;l) is M_(feed)×1 vector of MOS-DSSS navigation signals receivedfrom transmitted l. In the absence of nonlocal multipath, S_(R)(t;l) ismodeled by

$\begin{matrix}{{{s_{R}\left( {{t_{0} + t};\ell} \right)} \approx {e^{j2{\pi({{{\alpha_{TR}(\ell)}t} + {\frac{1}{2}{\alpha_{TR}^{(1)}(\ell)}t^{2}}})}}{g_{TR}(\ell)}\left( {{a_{TR}\left( {t;\ell} \right)} \circ {s_{T}\left( {{{\left( {1 - {\tau_{TR}^{(1)}(\ell)}} \right)t} - {\tau_{TR}(\ell)}};\ell} \right)}} \right)}},} & {{Eqn}(74)}\end{matrix}$where a_(TR)(t;l) is the M_(feed)×1 time-varying spatial signatureoperator with frequency response A_(TR)(f;l), which is also assumed toadhere to a first-order spatial signature blur model in presence ofchannel dynamics, due to both movement of the receiver over thereception interval, and adjustments in the yaw, pitch, and rollorientation of the receiver platform. Assuming the antennas have nonzerogain along right-hand and left-hand circular polarizations, and inabsence of local scattering multipath and channel dynamics, a_(TR)(t;l)can be modeled asA _(TR)(f;l)=A _(R)(f;Ψ _(R) u _(TR)(l))ρ_(TR)(l),  Eqn (75)where u_(TR)(l) is the observed line-of-bearing (LOB) direction vectorgiven in Eqn (15) and Ψ_(R) is a 3×3 rotation matrix that captures theyaw, pitch, and tilt of the receiver platform and converts the LOBvector to a local unit-norm direction-of-arrival (DOA) vector, in someaspects parameterized with respect to azimuth and elevation angles, andwhere

{A_(R)(f; u)}_(u₂ = 1) = {[A_(R)(f; u)❘_(RHCP)A_(R)(f; u)❘_(LHCP)]}_(u₂ = 1)is the array manifold of M_(feed)×2 complex gains along the right-handand left-hand circular polarizations at the BFN output, parameterizedwith respect to 3×1 unit-norm local direction-of-arrival (DOA) vector u,and ρ_(TR)(l) is a 2×1 unit-norm polarization gain vector. The arraymanifold can include adjustments to account for multipath local to thereceiver platform, mutual coupling between antenna elements, anddirection-independent complex gains in any distribution system couplingthe array to the BFN and/or the receiver bank.

As shown in FIG. 13 , each element of signal vector x_(R)(t) is thenchannelized into a K_(chn)×1 signal vector

x_(chn)(n_(sym); m_(feed)) = [x_(chn)(k_(chn), n_(sym); m_(feed))]_(k_(chn) = 0)^(K_(chn) − 1),using a bank of M_(feed) symbol-rate synchronous 1:K_(chn) vectorchannelizers (250), for example, using M_(feed) 1:M_(ADC) S/P operationsand K_(chn)×M_(ADC) channelization matrix operators T_(chn) (253), toform channelized signalx_(chn)(n_(sym);m_(feed))=T_(chn)∘[x_(R)(n_(sym)T_(sym)+m_(ADC)T_(ADC);m_(feed))].The M_(feed) channelizer output signals

{x_(chn)(n_(sym); m_(feed))}_(m_(feed) = 1)^(M_(feed))are then combined to form a single M_(chn)×1 complex vectorx_(chn)(n_(sym)) (259), where M_(chn)=K_(chn)M_(feed). In some aspectsof the invention, this is performed by “stacking” the signals first byreceiver feed, and then by channel, such that

$\begin{matrix}{{x_{chn}\left( n_{sym} \right)} = {\begin{pmatrix}\left\lbrack {x_{chn}\left( {0,{n_{sym};m_{feed}}} \right)} \right\rbrack_{m_{feed} = 1}^{M_{feed}} \\ \vdots \\\left\lbrack {x_{chn}\left( {{K_{chn} - 1},{n_{sym};m_{feed}}} \right)} \right\rbrack_{m_{feed} = 1}^{M_{feed}}\end{pmatrix}.}} & {{Eqn}(76)}\end{matrix}$In others, combining is performed first by channel, then by receiverfeed, such that

x_(chn)(n_(sym)) = [x_(chn)(n_(sym); m_(feed))]_(m_(feed) = 1)^(M_(feed)).Other, more general combining strategies can also be used; however, theform shown in Eqn (76) is has strong advantages for multi-subbandprocessing.

FIG. 14 depicts one aspect for performing multifeed, multi-subbandchannelization, using an FFT-based frequency channelization method. TheM_(feed)×1 vector ADC output signalx_(ADC)(n_(ADC))=x_(R)(T_(ADC)n_(ADC)) is passed through a bank ofM_(feed) 1:M_(ADC) serial-to-parallel (S/P) convertors (251) andoptionally windowed (153) symbol-rate synchronous FFT operations (252),each of which computes a K_(FFT)−bin FFT using M_(ADC) contiguoussamples of ADC output data, where f_(ADC)=M_(ADC)f_(sym). The FFToperation creates K_(FFT)M_(feed)×1 data vector

[x_(FFT)(k_(bin), n_(sym))]_(k_(bin) = 0)^(K_(FFT) − 1)with rate f_(sym) where

x_(FFT)(k_(bin), n_(sym)) = [x_(FFT)(k_(bin), n_(sym); m_(feed))]_(m_(feed) = 0)^(M_(feed)).

The FFT output vector is then passed through a subband selectionoperation (254), which selects K_(sub) subbands of FFT bins to formsubbands

{x_(DoF)(n_(sym); k_(sub))}_(k_(sub) = 0)^(K_(sub) − 1),each with rate f_(sym). In the aspect shown in FIG. 14 , each of thesubbands comprise M_(sub) FFT bins, such that x_(DoF)(n_(sym);k_(sub))is an

M_(DoF) × 1vectorgivenbyx_(DoF)(n_(sym); k_(sub)) = [x_(FFT)(k_(bin)(m_(sub); k_(sub)), n_(sym))]_(m_(sub) = 0)^(M_(sub) − 1),and where M_(DoF)=M_(sub)M_(feed). Other aspects may vary the number ofFFT bins in each subband, e.g., to account for interference loading orspectral shaping issues in each subband. In the aspect shown in FIG. 14, a “dense” subband selection strategy in whichk_(bin)(m_(sub);k_(sub))=(k_(init)(k_(sub))+m_(sub))mod K_(FFT) is alsoshown; however, as in the single-feed receiver, different strategies canbe used to form each subband set.

FIG. 15 depicts another aspect of the invention, in which the frequencychannelization is performed using a bank of polyphase filter basedsymbol-rate synchronous channelizers. The M_(feed)×1 vector ADC outputsignal x_(ADC)(n_(ADC))=x_(R)(T_(ADC)n_(ADC)) is passed through a bankof M_(feed) 1:M_(ADC) serial-to-parallel (S/P) convertors (251) and abank of M_(feed) polyphase filter based channelizers (255), each usingchannelizer weights {w_(chn)(m_(ADC))} (158), which creates aK_(chn)M_(feed)×1 data vector

[x_(chn)(k_(chn), n_(sym))]_(k_(chn) = 0)^(K_(chn) − 1)with rate f_(sym), where

x_(chn)(k_(chn), n_(sym)) = [x_(chn)(k_(chn), n_(sym); m_(feed))]_(m_(feed) = 0)^(M_(feed)).As in the single-feed channelizer shown in FIG. 10 , the frequencychannels are given by Eqn (21).

The K_(chn)M_(feed)×1 data vector is then put through a M_(DoF)×K_(sub)reshape operation (161), where K_(chn)=K_(sub)M_(sub), andM_(DoF)=M_(sub)M_(feed), such that K_(chn)M_(feed)=K_(sub)M_(DoF). Thiscreates K_(sub) subband signals

{x_(DoF)(n_(sym); k_(sub))}_(k_(sub) = 0)^(K_(sub) − 1),where M_(DoF)×1 subband k_(sub) signal

x_(DoF)(n_(sym); k_(sub)) = [x_(chn)(K_(sub)k_(sub) + m_(sub), n_(sym))]_(m_(sub) = 0)^(M_(sub) − 1).

FIG. 16 and FIG. 17 show exemplary values of K_(chn) and K_(sub), andM_(sub), designed to yield a constant value of M_(DoF)=60 as the numberof receiver feeds is varied from 1 to 6, for the GPS L1 legacy signal(FIG. 16 ) and the GPS L5 civil signal (FIG. 17 ). In all cases, thereceiver channelizer spans roughly 96% of the signal mainlobe, or justpast the half-power signal bandwidth. As the number of receiver feedsgrows, the number of frequency channels per subband is dropped, and thenumber of subbands is increased correspondingly, so that the degrees offreedom for linear-algebraic processing is the same in each subband, andthe multi-subband channelizer continues to occupy the same overallbandwidth.

The order-of-magnitude complexity in Mop/second and convergence time inmilliseconds is also shown in FIG. 16 and FIG. 17 . As these Figuresshow, the receiver complexity grows linearly with the number of receiverfeeds and bandwidth, and is well within the capabilities of low-cost DSPfor the L1 legacy signal, and moderate cost DSP for the GPS L5 signal.In contrast, the needed convergence time can be a low multiple of 60 msfor both signals and all receiver feeds. Moreover, the value of FIG. 16and FIG. 17 chosen here should be sufficient to detect and demodulateall of the GPS signals within the field of view of any terrestrialreceiver, with margin left over for detection and removal of pseudolitesand spoofers possibly impinging on the GPS band. Lastly, the multifeedreceiver should be able excise as many as M_(feed)−1 wideband non-GPSsignals, e.g., jammers, or as many as K_(sub)−1 narrowband jammers.

The channel model developed for the single-feed receiver also extends ina straightforward fashion to the multifeed receiver. Ignoring channeldynamics, the polyphase-filter based channelizer yields the samechannelized receive signal model given in Eqn (25), and the subbandmodel given in Eqn (58), where

$\begin{matrix}{{{a_{chn}(\ell)} \approx \left\lbrack {{a_{chn}\left( {{f_{chn}\left( k_{chn} \right)};\ell} \right)}{A_{TR}\left( {{f_{chn}\left( k_{chn} \right)};\ell} \right)}} \right\rbrack},} & {{Eqn}(77)}\end{matrix}$ $\begin{matrix}{{{a_{DoF}\left( {k_{sub};\ell} \right)} \approx {\left\lbrack {a_{chn}\left( {{f_{chn}\left( {K_{sub} + m_{sub}} \right)};\ell} \right)} \right\rbrack_{m_{sub} = 0}^{M_{sub} - 1} \otimes {A_{TR}\left( {{f_{sub}\left( k_{sub} \right)}\ell} \right)}}},} & {{Eqn}(78)}\end{matrix}$and where a_(chn)(f_(chn)(k_(chn));l) is given by Eqn (40)-Eqn (41) and“⊗” denotes the Kronecker product operation. Similarly, the per-channeland per-subband interference ACM is given by

$\begin{matrix}{{{R_{i_{chn}i_{chn}}\left( k_{chn} \right)} \approx {\frac{M_{ADC}^{2}}{M_{chp}}f_{chp}{diag}\left\{ {{❘{H_{R}\left( {f_{chn}\left( k_{chn} \right)} \right)}❘}^{2}{S_{i_{R}i_{R}}\left( {f_{chn}\left( k_{chn} \right)} \right)}} \right\}_{k_{sub},{= 0}}^{K_{sub} - 1}}},} & {{Eqn}(79)}\end{matrix}$ $\begin{matrix}{{{R_{i_{DoF}i_{DoF}}\left( k_{sub} \right)} \approx {\frac{M_{ADC}^{2}}{M_{chp}}f_{chp}{❘{H_{R}\left( {f_{sub}\left( k_{sub} \right)} \right)}❘}^{2}\left( {P_{sub} \otimes {S_{i_{R}i_{R}}\left( {f_{sub}\left( k_{sub} \right)} \right)}} \right)}},} & {{Eqn}(80)}\end{matrix}$where S_(i) _(R) _(i) _(R) (f) is the M_(feed)×M_(feed) matrix powerspectral density of i_(R)(t).

Importantly, while the TOA and FOA of a GNSS transmitter can be easilyspoofed in a covert or “aligned” spoofing scenario, the DOA (and, to alesser degree, the polarization) of that transmitter cannot be easilyspoofed. In addition, the multi-feed receiver can null any CCI impingingon the array, if the array has sufficient degrees of freedom to separatethat CCI from the GNSS signals.

In presence of channel dynamics, the local signal DOA adheres closely toa first-order model over time intervals on the order of 10 seconds insome aspects of the invention, and the individual subbands willexperience additional signature blur due to the changing TOA, LOB, and(typically more importantly, due to dependence on changing receiverplatform orientation) DOA of the transmitters and receiver. Thissignature blur is likely to further load the subbands with low-levelsignature components that will be excised by subsequent linear combiningoperations. In this regard, the effect of TOA changes is reducedsubstantively for the multifeed symbol-rate synchronous sub-bandchannelizer shown in FIG. 15 , due to the narrower subband channelsobtaining as the number of receiver feeds is increased, as shown in FIG.16 and FIG. 17 .

Resilient PNT Signal Processing Methods

A common set of signal processing methods can be applied to dataprovided by all of the single-feed and multifeed receiver structures andsymbol-rate synchronous channelization and multi-subband formationoperations described above. In particular, in-subband linear combiningweights approaching the max-SINR solution can be computed usinglinear-algebraic methods disclosed in the '417 NPA, given any of thefollowing:

-   -   Knowledge of the content of {d_(T)(n_(sym);l)}_(l=1) ^(L) ^(T) ,        e.g., from navigation data or symbol sequences provided by        third-party sources.    -   Knowledge of a component of {d_(T)(n_(sym);l)}_(l=1) ^(L) ^(T) ,        e.g., known or periodic pilot signals, as listed in FIG. 4 for        the GPS civil L5, QZSS, Galileo E5AB, E6B E6C, and NAVIC RS BOC        signals    -   Other exploitable structure of {d_(T)(n_(sym);l)}_(l=1) ^(L)        ^(T) , e.g., real or BPSK structure, as listed in FIG. 4 for the        GLONASS and GPS L1 legacy signals; QPSK structure, as listed in        FIG. 4 for the Beidou 1B and NAVIC SPS-L5 and SPS-S signals; and        constant modulus structure, as listed in FIG. 4 for all of the        GNSS signals.        These methods also can be used to estimate the max-SINR        obtaining in each subband, thereby providing cross-subband        weights for the second combining stage shown in Eqn (64). The        multi-subband solution can further be used to estimate the full        max-SINR of the received symbol sequences, detect the navigation        signals in the environment, determine at least the        geo-observables {n_(TR)(l),{tilde over (α)}_(TR)(l)}_(l=1) ^(L)        ^(T) for those signals, and if needed estimate        information-bearing components of the transmitted symbol streams        {d_(T)(n_(sym);l)}_(l=1) ^(L) ^(T) . Moreover, these techniques        can perform these operations without prior knowledge of the        signal ranging code or receive frequency signature for the        signals, or a search over TOA and FOA is the ranging code is        known.

In addition, the '417 NPA discloses means for estimating the fine TOA,FOA Nyquist zone, and DFOA using additional copy-aided parameterestimation algorithms. Lastly, the data model derived above can be usedto develop matched-filtering methods, using estimates of a_(chn)(l)given in Eqn (40)-Eqn (41) for single-receiver systems, or defined inEqn (77) for multi-receiver systems.

The signal processing structures can be adapted on either a continuousbasis, in which geo-observables are updated rapidly over time, or on abatch processing basis, in which a block of N_(sym) channelized datasymbols

{x_(DoF)(n_(sym); k_(sub))}_(n_(sym) = 0)^(N_(sym) − 1)are computed for each subband and passed to a DSP processing elementthat detects the GNSS signals within that data block. The latterapproach is especially useful if the invention is being used to developresilient PNT analytics to aid a primary navigation system, e.g., toassess quality and availability of new GNSS transmissions, or to detector confirm spoofing transmissions on a periodic basis. The batchadaptive processing algorithms are described in more detail below.Batch Adaptive Processing Procedure

In the batch adaptive processing procedure is implemented by firstcollecting data over N_(sym) data symbols, and detecting, extracting, orestimating geo-observables of the MOS-DSSS symbol or navigationsequences directly from that data set. In some aspects, the procedureperforms this processing from a “cold start,” i.e., with no priorinformation about the signals contained within that data set. However,if the prior FOA's of the signals (and in particular FOA's derived fromthe FOA vectors for those signals) are known, then the procedure can bestarted at an intermediate point in the processing.

This procedure enables a great deal of refinement and accuratediscrimination to more closely constrain and limit the processingnecessary to accurately interpret the signal's content, before thecopy-aided analysis phase begins. In some use scenarios, the blinddespreading stage can in fact obviate the copy-aided analysis phase,e.g., if the invention is developing resilient PNT analytics to aid aprimary navigation system, or it can be used to substantively thin thenumber of transmissions that must be analyzed. This procedure canthereby reduce the processing complexity and considerable feedback lag,enabling quicker, more effective signal discrimination without requiringthe full processing and analysis of the signal be completed first (oreven together).

FIG. 18 is a flow diagram of a fully-blind multi-subband signaldetection, geo-observable/quality estimation, and symbol estimationbatch procedure that can be employed for MOS-DSSS signals with BPSK (or,more generally, real) symbol sequences, e.g., the GLONASS and GPS L1legacy signal, or LocataLite beacons. Upon receipt of N_(sym) symbols ofdata (300), e.g., N_(sym) milliseconds of receive data for the GNSSsignals depicted in FIG. 4 , the procedure first channelizes the dataand forms it into K_(sub) subbands using a symbol-rate synchronouschannelizer (301). In some aspects, the data subbands are formed intoK_(sub) data matrices with dimension N_(sym)×M_(DoF), e.g., given by

$\begin{matrix}{{{X_{DoF}\left( k_{sub} \right)}\overset{\Delta}{=}\begin{pmatrix}{\sqrt{\omega_{DoF}(0)}{x_{DoF}^{H}\left( {0;k_{sub}} \right)}} \\ \vdots \\{\sqrt{\omega_{DoF}\left( {N_{sym} - 1} \right)}{x_{DoF}^{H}\left( {{N_{sym} - 1};k_{sub}} \right)}}\end{pmatrix}},} & {{Eqn}(81)}\end{matrix}$where

{ω_(DoF)(n_(sym))}_(n_(sym) = 0)^(N_(sym) − 1)is a real data window satisfying

${\sum\limits_{n_{sym} = 0}^{N_{sym} - 1}{\omega_{DoF}\left( n_{sym} \right)}} = 1.$

The channelized subband data matrices

{X_(DoF)(k_(sub))}_(k_(sub) = 0)^(K_(sub) − 1)are then whitened (302), e.g., by performing the QR decomposition (QRD)of each subband matrix, to form whitened subband matrices

{Q_(DoF)(k_(sub))}_(k_(sub) = 0)^(K_(sub) − 1).The QRD, denoted {Q,R}=QRD(X) for general N×M matrix X, solves

$\begin{matrix}{{R = {{chol}\left\{ {X^{H}X} \right\}}},} & {{Eqn}(82)}\end{matrix}$ $\begin{matrix}{{Q = {{XR}^{- 1} = \begin{pmatrix}{q^{H}(0)} \\ \vdots \\{q^{H}\left( {N - 1} \right)}\end{pmatrix}}},} & {{Eqn}(83)}\end{matrix}$where chol(⋅) is the Cholesky factorization operation, such that X=QRand Q^(H)Q=I_(M) where I_(M) M×M identity matrix. The data window isnominally rectangular; however, other windows are recommended if the FOAoffset between the navigation signals is small, e.g., for fixed groundbeacons or aligned spoofers, or for reception intervals that are longenough to induce substantive differential FOA effects.

For navigation signals in which only a single rail is modulated, e.g.,GLONASS or GPS L1 legacy signals, the subbands can be processed usingthe conjugate self-coherence restoral (CSCORE) method disclosed in the'417 NPA. For the multi-subband method, CSCORE statistics are developedwithin each subband, and combined to form a cross-subband statistic(303) that simultaneously detects the signals, and provides an estimatethe fine FOA and quality of each signal. In one aspect, the CSCOREalgorithm is implemented in each subband for a trial FOA vector

${\alpha = \begin{bmatrix}\alpha & \alpha^{(1)}\end{bmatrix}^{T}},$by first computing

Q_(DoF)(α; k_(sub)) = Δ(α)Q_(DoF)(k_(sub)),${{\Delta(\alpha)}\overset{\Delta}{=}{{diag}\left\{ {\exp\left( {j2\pi{{\mathcal{g}}_{FOA}\left( n_{sym} \right)}\alpha} \right)} \right\}_{n_{sym} = 0}^{N_{sym} - 1}}},$where g_(FOA)(n_(sym))=[n_(sym) ½n_(sym) ²]; forming whitened CSCOREmatrix

R̂_(q_(DoF)q_(DoF)^(*))(α; k_(sub))given by

$\begin{matrix}\begin{matrix}{{{\hat{R}}_{q_{DoF}q_{DoF}^{*}}\left( {\alpha;k_{sub}} \right)} = {\sum\limits_{n_{sym} = 0}^{N_{sym} - 1}{{q_{DoF}\left( {n_{sym};k_{sym}} \right)}{q_{DoF}^{T}\left( {n_{sym};k_{sym}} \right)}{\exp\left( {{- j}4\pi{{\mathcal{g}}_{FOA}^{T}\left( n_{sym} \right)}\alpha} \right)}}}} \\{{= {\sum\limits_{n_{sym} = 0}^{N_{sym} - 1}{{q_{DoF}\left( {n_{sym};\alpha;k_{sub}} \right)}{q_{DoF}^{T}\left( {n_{sym};\alpha;k_{sub}} \right)}}}},} \\{= {{Q_{DoF}^{H}\left( {\alpha;k_{sub}} \right)}{Q_{DoF}^{*}\left( {\alpha;k_{sub}} \right)}}}\end{matrix} & {{Eqn}(84)}\end{matrix}$for each subband; and determining the dominant mode{λ_(CSC)(α;k_(sub)),v_(CSC)(α;k_(sub))} of the singular valuedecomposition (SVD) of

R̂_(q_(DoF)q_(DoF)^(*))(α; k_(sub)),e.g., using a power method. The detection statistics

{λ_(CSC)(α; k_(sub))}_(k_(sub) = 0)^(K_(sub) − 1)are then combined across the subbands to form a full-band CSCOREstatistic. In one aspect on the invention, this is accomplished by firstcomputing max-SINR estimateγ_(CSC)(α;k_(sub))=(1+λ_(CSC)(α;k_(sub)))/(1−λ_(CSC)(α;k_(sub))) foreach subband, and summing those estimates together for each FOA vectorα. In other aspects, nonlinear combining operations, e.g., dictated bymaximum-likelihood (ML) estimation arguments are performed. In otheraspects, the combining is performed over values of α that are adjustedto account for DTOA between subbands.

This procedure generates a CSCORE spectrum that is parameterized withrespect to both FOA (or DTOA) and DFOA. This spectrum is then used todetect the MOS-DSSS signals in the environment, and estimate their FOA(or DTOA) and DFOA geo-observables (304). Additional joint processing isthen performed to further improve quality of the geo-observables and thedetection statistic (305), resulting in optimized DTOA and DFOAestimates {{circumflex over (τ)}_(CSC) ⁽¹⁾(l),{circumflex over(α)}_(CSC) ⁽¹⁾(l)}_(l=1) ^({circumflex over (L)}) ^(T) for the{circumflex over (L)}_(T) detected signals, and resulting in optimizeddespreading weights {v_(CSC)(α(k_(sub);l));k_(sub)}_(l=1)^({circumflex over (L)}) ^(T) for each subband, whereα(k_(sub);l)=[−{circumflex over (τ)}_(CSC)⁽¹⁾(l)(f_(T)+f_(sub)(k_(sub))) {circumflex over (α)}_(CSC) ⁽¹⁾(l)]^(T).

The optimized despreading weights and estimated FOA vector are then usedto despread and despin the symbol sequence for each detected signal, andto demodulate the underlying signal navigation sequence based on furtherstructure of that sequence, e.g., 20:1 NAV bit replication for the GPSL1 legacy signal (306). As part of this process, the coarse TOA timingis computed to within a NAV bit edge.

Given reception of sufficient data, the NAV signal is analyzed toresolve the ±1 ambiguity in the spread signal; detect NAV blockboundaries to determine the full coarse TOA; and if needed extract thesatellite ephemeres from the NAV signal sequences (307). In someaspects, this is accomplished by processing of data over multiplereception blocks. In other aspects, this is accomplished by shifting toa continuous update (non-batch) processing mode.

In some aspects, the ranging code and (for multifeed receivers) arraymanifold are downloaded from memory (310), and used to determine thefull TOA, FOA, DOA, and (using estimated and/or on-board orientationdata) LOB of the detected signals, and determine a positioning,navigation, and timing (PNT) solution for the receiver (308). In otheraspects, the fine FOA (or TDOA) and DFOA, and transmitter ephemeres aresufficient to determine a positioning, navigation and frequencysynchronization solution for the receiver.

FIG. 19 is a flow diagram of a multi-subband signal detection andgeo-observable/quality estimation, algorithm that can be employed in aresilient PNT data analytics engine (RPNT-AE) aspect of the invention.Upon receipt of an RPNT-AE trigger (319), e.g., initiated by a primaryGNSS processor, or by other processes on board and/or connected to thereceiver, the RPNT-AE process is begun (320). The RPNT-AE processor thentasks a receiver to obtain and store a snapshot of N_(sym) data symbols,and obtains a time/frequency stamp recording rough (to within receiverclock accuracy) center frequency and start time of the snapshot, andother information available to the receiver, e.g., receiver orientation(321). The RPNT-AE processor then places the time/frequency stamped datainto memory (310), and sends the stamp to an external resource (322 a)along with a request for third-party data. The RPNT-AE processor thenwaits until an external resource (322 b) provides the processor with asnapshot of navigation (NAV/CNAV) data covering the time period andfrequency band recorded in the time/frequency stamp, and (if needed) atransmitter almanac containing the ephemeres of the transmitters overthe time period covering the NAV/CNAV data. Once RPNT-AE processorobtains that data (323), it places that data in memory (310) and sends a“Data Ready” flag is sent to the DSP processor tasked with estimatingRPNT analytics for the processor.

Once the Data Ready flag is obtained from the RPNT-AE processor, the DSPresources obtain the time/frequency stamped received data snapshot andthe NAV/CNAV data from memory (310), and generate RPNT analytics usingpartially blind methods disclosed in the '417 NPA, e.g., an“FFT-least-squares” algorithm or a single-target or multi-targetmaximum-likelihood estimator, the DSP processor. Analytics measure herecan include the following:

-   -   estimates of observed received parameters of navigation signals,        including signal geo-observables usable to obtain PNT solutions        for the reception platform, e.g., observed signal        frequency-of-arrival (FOA), time-of-arrival (TOA), and observed        local direction-of-arrival (DOA) or global line-of-bearing (LOB)        in systems employing multifeed receivers;    -   estimates of received signal quality, e.g., received incident        power, and of despread/demodulated navigation sequence quality,        e.g., despreader output signal-to-interference-and-noise ratio        (SINR); and    -   measures of accuracy of parameter and signal quality estimates.        RPNT analytic measurement methods include “partially-blind”        methods that do not require knowledge of the ranging code for        the navigation signals, or spatial/polarization array-manifold        data (measurement of cross-feed spatial/polarization signatures        as a function of DOA) for the receiver, and “copy-aided” methods        that may require one or both of the ranging codes or the array        manifold to provide more complete RPNT analytics. In the aspects        disclosed herein, RPNT analytics are further computed over        multiple subbands.

Once the RPNT analytics have been obtained, the RPNT-AE process is ended(325), and the RPNT analytics are reported to the resources requestingthe analytics.

FIG. 20 is a block diagram of a multi-subband pilot-exploiting RPNT(PE-RPNT) processor that can detect and estimate geo-observables andquality of MOS-DSSS signals in which known or repeating pilotstransmitted as part of the MOS-DSSS system sequence. The method reportedherein can also be used to implement the operations performed by theRPNT-AE DSP processor (324), using the full MOS-DSSS symbol sequenceprovided in that system.

Upon receipt of N_(sym) symbols of data (300), e.g., N_(sym)milliseconds of receive data for the GNSS signals depicted in FIG. 4 ,the procedure first channelizes the data and forms it into K_(sub)subbands using a symbol-rate synchronous channelizer (301). In someaspects, the data subbands are formed into K_(sub) data matrices withdimension N_(sym)×M_(DoF), e.g., given by Eqn (81). The channelizedsubband data matrices

{X_(DoF)(k_(sub))}_(k_(sub) = 0)^(K_(sub) − 1)are then whitened (302), e.g., by performing the QR decomposition (QRD)of each subband matrix, to form whitened subband matrices

{Q_(DoF)(k_(sub))}_(k_(sub) = 0)^(K_(sub) − 1).

The processor then retrieves a single period of repeating pilot data

{p(n_(sym))}_(n_(sym) = 0)^(N_(pilot) − 1)from memory (310), where N_(pilot) is the period of the pilot sequence;computes pilot statistics over a set of trial FOA vectors

$\alpha = \begin{bmatrix}\alpha & \alpha^{(1)}\end{bmatrix}^{T}$trial pilot delay m_(pilot)∈{0, . . . , N_(pilot)−1} in each subband,given by least-squares (LS) whitened linear combiner weights

$\begin{matrix}\begin{matrix}{{u_{LS}\left( {\alpha,{m_{pilot};k_{sub}}} \right)} = {\sum\limits_{n_{sym} = 0}^{N_{sym}}{{q_{DoF}\left( {n_{sym};k_{sub}} \right)}{d_{LS}^{*}\left( {{n_{sym};\alpha},m_{pilot}} \right)}}}} \\{{= {{Q_{DoF}^{H}\left( k_{sub} \right)}{d_{LS}\left( {\alpha,m_{pilot}} \right)}}},}\end{matrix} & {{Eqn}(85)}\end{matrix}$${d_{LS}\left( {{n_{sym};\alpha},m_{sym}} \right)} = {\sqrt{\omega_{DoF}\left( n_{sym} \right)}{p\left( {\left( {n_{sym} - m_{pilot}} \right){mod}N_{pilot}} \right)}e^{j2\pi{{\mathcal{g}}_{FOA}(n_{sym})}\alpha}}$$\begin{matrix}{{{d_{LS}\left( {\alpha,m_{sym}} \right)} = \begin{pmatrix}{d_{LS}^{*}\left( {{0;\alpha},m_{sym}} \right)} \\ \vdots \\{d_{LS}^{*}\left( {{{N_{sym} - 1};\alpha},m_{sym}} \right)}\end{pmatrix}},} & {{Eqn}(86)}\end{matrix}$where g_(FOA)(n_(sym))=[n_(sym) ½n_(sym) ²], and in-band LS SINRestimate,

$\begin{matrix}{{{\gamma_{LS}\left( {\alpha,{m_{pilot};k_{sub}}} \right)} = \frac{{{u_{LS}\left( {\alpha,{m_{pilot};k_{sub}}} \right)}}_{2}^{2}}{1 - {{u_{LS}\left( {\alpha,{m_{pilot};k_{sub}}} \right)}}_{2}^{2}}};} & {{Eqn}(87)}\end{matrix}$and combines the in-subband least-square SINR estimates to created amulti-subband quality statistic as a function of FOA vector and pilotdelay (333). In one aspect, the in-subband LS SINR estimates arecombined in accordance with a maximum-likelihood estimator, yieldingmulti-subband quality statistic

$\begin{matrix}{{{S_{ML}\left( {\alpha,m_{pilot}} \right)} = {\sum\limits_{k_{sub} = 0}^{K_{sub} - 1}{\log\left( {1 + {\gamma_{LS}\left( {\alpha,{m_{pilot};k_{sub}}} \right)}} \right)}}},} & {{Eqn}(88)}\end{matrix}$which is maximized at modulo-N_(pilot) coarse TOA's and fine FOA vectorspossessed by the MOS-DSSS signals in the receivers field of view. Inanother aspect, the in-subband LS SINR estimates are combined inaccordance with Eqn (65), yielding multi-subband ML quality statistic

$\begin{matrix}{{{S_{LS}\left( {\alpha,m_{pilot}} \right)} = {\sum\limits_{k_{sub} = 0}^{K_{sub} - 1}{\gamma_{LS}\left( {\alpha,{m_{pilot};k_{sub}}} \right)}}},} & {{Eqn}(89)}\end{matrix}$which is also maximized at modulo-N_(pilot) coarse TOA's and fine FOAvectors possessed by the MOS-DSSS signals in the receiver's field ofview. In other aspects, the effect of DTOA across frequency subbands istaken into account, e.g., resulting in DTOA-corrected multi-subband LSquality statistic

$\begin{matrix}{{{S_{LS}\left( {\tau^{({1,2})},m_{pilot}} \right)} = {\sum\limits_{k_{sub} = 0}^{K_{sub} - 1}{\gamma_{LS}\left( {{\alpha\left( k_{sub} \right)},{m_{pilot};k_{sub}}} \right)}}},} & {{Eqn}(90)}\end{matrix}$ $\begin{matrix}{{\tau^{({1,2})} = \begin{pmatrix}\tau^{(1)} \\{\overset{\sim}{\tau}}^{(2)}\end{pmatrix}},} & {{Eqn}(91)}\end{matrix}$ $\begin{matrix}{{{\alpha\left( k_{sub} \right)} = {- \left( {f_{T} + {f_{sub}\left( k_{sub} \right)}} \right)T_{sym}\tau^{({1,2})}}},} & {{Eqn}(92)}\end{matrix}$where {tilde over (τ)}⁽²⁾=τ⁽²⁾T_(sym) is the symbol-normalizeddifferential DTOA. In addition, for rectangular time windows, thein-band LS SINR estimate can be converted to unbiased max-SINR estimate

$\begin{matrix}{{{{\hat{\gamma}}_{\max - {SINR}}\left( {\alpha,{m_{pilot};k_{sub}}} \right)} = {{\left( {1 - \frac{M_{DoF} + 1}{N_{sym}}} \right){\gamma_{LS}\left( {\alpha,{m_{pilot};k_{sub}}} \right)}} - M_{DoF}}},} & {{Eqn}(93)}\end{matrix}$which can greatly improve visible quality of S_(LS)(α,m_(pilot)) (orS_(LS)(τ^((1,2));m_(pilot))) without affecting performance of thestatistic.

A number of means can be used to minimize efficiency of the in-subbandLS SINR's and multi-subband quality statistics. In particular, FFT-basedmethods can be used to efficiently compute γ_(LS)(α,m_(pilot);k_(sub))or γ_(LS)(α(k_(sub))m_(pilot);k_(sub)) with fine accuracy. At this stageof processing, the whitened LS weights given in Eqn (85) need not becomputed, further reducing complexity and memory requirements of theoverall processor.

The multi-subband quality statistic is then analyzed to detect thepilot-bearing MOS-DSSS signals in the environment, determine theircoarse TOA to modulo-N_(pilot) accuracy, and determine their fine FOA orDTOA vector (334), resulting in {circumflex over (L)}_(T) peakdetections and FOA-TOA locations {α(l),m_(pilot)(l)}_(l=1)^({circumflex over (L)}) ^(T) or DTOA-TOA locations{τ^((1,2))(l),m_(pilot)(l)}_(l=1) ^({circumflex over (L)}) ^(T) of thosepeaks. Iterative refinement of the DTOA-TOA locations{τ^((1,2))(l),m_(pilot)(l)}_(l=1) ^({circumflex over (L)}) ^(T) (wherethe FOA vector is converted to a DTOA vector) is then performed (335),e.g., using Newton search methods disclosed in the '417 NPA, todetermine the fine DTOA vector (from which FOA can be derived) andoptimize the multi-subband quality statistic.

Using the optimized DTOA vectors and modulo-N_(pilot) coarse TOA's{τ^((1,2))(l),m_(pilot)(l)}_(l=1) ^({circumflex over (L)}) ^(T) , LScombiner weights {γ_(LS)(k_(sub);l),u_(LS)(k_(sub);l)} are then computedusing formula

$\begin{matrix}{{{u_{LS}\left( {k_{sub};\ell} \right)} = {\sum\limits_{n_{sym} = 0}^{N_{sym}}{{q_{DoF}\left( {n_{sym};k_{sub}} \right)}{d_{LS}^{*}\left( {{n_{sym};{\alpha\left( {k_{sub};\ell} \right)}},{m_{pilot}(\ell)}} \right)}}}},} & {{Eqn}(94)}\end{matrix}$ $\begin{matrix}{{{\alpha\left( {k_{sub};\ell} \right)} = {- \left( {f_{T} + {f_{sub}\left( k_{sub} \right)}} \right)T_{sym}{\tau^{({1,2})}(\ell)}}},} & {{Eqn}(95)}\end{matrix}$ $\begin{matrix}{{{\gamma_{LS}\left( {k_{sub};\ell} \right)} = \frac{{{u_{LS}\left( {k_{sub};\ell} \right)}}_{2}^{2}}{1 - {{u_{LS}\left( {k_{sub};\ell} \right)}}_{2}^{2}}},} & {{Eqn}(96)}\end{matrix}$and cross-subband combiner gains are computed based on Eqn (64), i.e.,by setting g_(LS)(k_(sub);l)=1+γ_(LS)(k_(sub);l) The full multi-subbanddespread, despun and partially time-synchronized symbol sequence is thenestimated for each peak using formula

$\begin{matrix}{{{{\hat{d}}_{T}\left( {n_{sym};\ell} \right)} = {\sum\limits_{k_{sub} = 0}^{K_{sub} - 1}{{{\mathcal{g}}_{LS}^{*}\left( {k_{sub};\ell} \right)}{{\hat{d}}_{T}\left( {n_{sym};k_{sub};\ell} \right)}}}},} & {{Eqn}(97)}\end{matrix}$ $\begin{matrix}{{{\hat{d}}_{T}\left( {n_{sym};k_{sub};\ell} \right)} = {\left( {{u_{LS}^{H}\left( k_{sub} \right)}{q_{DoF}\left( {{n_{sym} + {m_{pilot}(\ell)}};\ell} \right)}} \right){e^{- j2\pi{{\mathcal{g}}_{FOA}(n_{sym})}{\alpha({k_{sub};\ell})}}.}}} & {{Eqn}(98)}\end{matrix}$The navigation-bearing component of the symbol sequence (CNAV for theGPS L5 signal) is then demodulated using information about the structureof the navigation data (346).

Given reception of sufficient data, the CNAV signal is analyzed todetermine the full coarse TOA, and if needed extract the satelliteephemeres from the NAV signal sequences (347). In some aspects, this isaccomplished by processing of data over multiple reception blocks. Inother aspects, this is accomplished by shifting to a continuous update(non-batch) processing mode.

In some aspects, the ranging code and (for multifeed receivers) arraymanifold are downloaded from memory (310), and used to determine thefull TOA, FOA, DOA, and (using estimated and/or on-board orientationdata) LOB of the detected signals, and determine a positioning,navigation, and timing (PNT) solution for the receiver (308). In otheraspects, the fine FOA (or TDOA) and DFOA, and transmitter ephemeres aresufficient to determine a positioning, navigation and frequencysynchronization solution for the receiver.

FIG. 21 is a flow diagram of a local-maxima search procedure accordingto an aspect of the disclosure, which is applicable to searches over FOAand DFOA, over reception intervals in which DFOA can have a substantiveeffect on detection sensitivity. The approach assumes the use of anFFT-based coarse search procedure, in which α is defined over searchgrid

$\begin{matrix}{{{\overset{\sim}{\alpha}\left( k_{bin} \right)} = {k_{bin}/K_{bin}}},{k_{bin} = 0},\ldots,{K_{bin} - 1},} & {{Eqn}(99)}\end{matrix}$ $\begin{matrix}{{{{{{\overset{\sim}{\alpha}}_{TR}^{(1)}\left( k_{tile} \right)} = {\overset{\sim}{\alpha}}_{TR}^{(1)}}❘}_{\max}\left( {\frac{{2k_{tile}} + 1}{K_{tile}} - 1} \right)},{k_{tile} = 0},\ldots,{K_{tile} - 1},} & {{Eqn}(100)}\end{matrix}$where K_(bin) is the number of FOA bins searched over, and K_(tile) isthe number of DFOA tiles searched over. Then the multi-subband qualityestimate can be given by 3-dimensional surface

$\begin{matrix}{{{S_{LS}\left( {k_{bin},k_{tile},m_{pilot}} \right)} = {\sum\limits_{k_{sub} = 0}^{K_{sub} - 1}{\gamma_{LS}\left( {k_{bin},k_{tile},{m_{pilot};k_{sub}}} \right)}}},} & {{Eqn}(101)}\end{matrix}$ $\begin{matrix}{{{\gamma_{LS}\left( {k_{bin},k_{tile},{m_{pilot};k_{sub}}} \right)} = \frac{{{u_{LS}\left( {k_{bin},k_{tile},{m_{pilot};k_{sub}}} \right)}}_{2}^{2}}{1 - {{u_{LS}\left( {k_{bin},k_{tile},{m_{pilot};k_{sub}}} \right)}}_{2}^{2}}},} & {{Eqn}(102)}\end{matrix}$ $\begin{matrix}\begin{matrix}{{u_{LS}\left( {k_{bin},k_{tile},{m_{pilot};k_{sub}}} \right)} = {\sum\limits_{n_{sym} = 0}^{N_{sym} - 1}{{q_{DoF}\left( {n_{sym};k_{sub}} \right)}{d_{LS}^{*}\left( {{n_{sym};k_{tile}},m_{pilot}} \right)}e^{- j2\pi k_{bin}n_{sym}/K_{bin}}}}} \\{{= {{DFT}\left\{ {{q_{DoF}\left( {n_{sym};k_{sub}} \right)}{d_{LS}^{*}\left( {{n_{sym};k_{tile}},m_{pilot}} \right)}} \right\}}},}\end{matrix} & {{Eqn}(103)}\end{matrix}$ $\begin{matrix}{{{d_{LS}\left( {{n_{sym};k_{tile}},m_{pilot}} \right)} = {e^{j\pi{{\overset{\sim}{\alpha}}^{(1)}(k_{tile})}n_{sym}^{2}}{p\left( {\left( {n_{sym} - m_{pilot}} \right){mod}N_{pilot}} \right)}}},} & {{Eqn}(104)}\end{matrix}$which can be implemented using K_(tile)N_(pilot) DFT operations.

Returning to FIG. 21 , once the search is started (350), the number ofDFOA search tiles K_(tile) first is determined based on the expectedrange in DFOA and the reception time. Then an initial DFOA search tileis chosen (351), and a DFT-based search is conducted over that tileusing Eqn (101)-Eqn (104), to compute a multi-subband search spectrumfor that tile, and determine peaks in that tile (352).

Once all of the DFOA tiles have been searched, and peaks have beendetermined, the detected peaks are thinned to a significant number ofpeaks based on peak value (353). Then the peak values are iterivaleyoptimized using local optimization methods, e.g., quadratic fit to thepeak maximum, followed by Newton or Gauss-Newton search methods (354).In this case, m_(pilot) is defined over an integer set of values, henceit is not iteratively optimized using this procedure.

In one aspect of the invention, the local optimization is performed tooptimize

$\begin{matrix}{{{S_{LS}(\ell)} = {\sum\limits_{k_{sub} = 0}^{K_{sub} - 1}{\gamma_{LS}\left( {k_{sub};\ell} \right)}}},} & {{Eqn}(105)}\end{matrix}$where γ_(LS)(k_(sub);l) is given by Eqn (94)-Eqn (96), and where{τ^((1,2))(l),m_(pilot)(l)}_(l=1) ^({circumflex over (L)}) ^(T) is theparameter set being optimized. In this case, τ^((1,2))(l) is initializedusing the optimal value of α(l) determined during the FFT-based searchprocedure.

Once optimal values have been determined, ancillary RPNT statistics arecomputed at those optimal search locations (355). The search is thenended (356).

FIGS. 22A, 22B, and 22C and FIGS. 23A, 23B, and 23C depict DFOA searchsensitivity as a function of the number of DFOA search tiles, for a ±3Hz/s DFOA range, consistent with DFOA's expected for a MEO satelliteconstellation. FIGS. 22A, 22B, and 22C show search sensitivity relativeto 0 Hz/s for a rectangular time window, and for a ½ second (FIG. 22A),1 second (FIG. 22B), and 2 second (FIG. 22C) reception interval. Asshown in FIGS. 22A, 22B, and 22C, the number of search tiles needed tominimize sensitivity loss grows rapidly with reception time. FIGS. 23A,23B, and 23C show equivalent search sensitivity for a Nuttall timewindow, which has a time-bandwidth product (TBP) that is roughly halfthe value of the rectangular window. The Nuttall window can reduce thenumber of tiles required to perform an effective search at a 2 secondreception time. However, this is offset by the lower TBP of the window.

While this invention is susceptible of instantiation in many differentforms, there are shown in the drawings and described in detail in thetext of Provisional Appl. No. 62/773,589, incorporated herein byreference, and Provisional Appl. No. 62/773,605, incorporated herein byreference, several specific aspects of the invention, with theunderstanding that the present disclosure is to be considered as anexemplification of the principles of the invention and is not intendedto limit the invention to the aspects illustrated.

In an aspects applicable to all of the approaches above, the inventionobtains snapshots of baseband navigation data covering the time intervalof data collected by the receiver, and symbol-synchronously channelizedby the invention, and uses that baseband navigation data to implementnon-fully-blind demodulation algorithms. The resultant aspects canprovide extreme high precision of FOA, TOA, and DFOA/DTOA driftestimates; assess integrity of data collected by the host platform; andprovide other functions of interest to the user. When coupled with acommunication channel allowing the receive data to be transported to acentral processor, the invention can also allow implementation of allfunctions at off-line resources, thereby eliminating all DSP complexityassociated with the algorithms. The aspects can also be used toimplement signal cancellation algorithms that detect signals under theknown navigation signals, e.g., for purposes of spoofer and jammerdetection.

Any reception operation used in the invention can be implemented usingany of the set of one or more dedicated receivers and software definedradios (SDR) either separate from or integrated with antennas,amplifiers, mixers, filters, analog-to-digital converters (ADC's) andsignal processing gear.

Operations Processing used in each of the inventions above can beimplemented in any combination of hardware and software, fromspecial-purpose hardware including any of application-specificintegrated circuits (ASIC's) and field-programmable gate arrays(FPGA's); firmware instructions in a lesser-specialized set of hardware;embedded digital signal processors (e.g. Texas Instrument or AdvancedRisc Machine DSP's); graphical processing units (GPU's); vector,polynomic, quantum, and other processors; and in any combination or soleuse of serial or parallel processing; and on general-purpose computersusing software instructions.

Operations Processing used in each of the inventions above can befurther implemented using any set of resources that are on-board,locally accessible to, and remotely accessible by the receiver aftertransport of the data and instructions to be processed by any of asingle computer, server, and set of servers, and then directed onwards,using any number of wired or wireless means for such transport.

Some of the above-described functions may be composed of instructions,or depend upon and use data, that are stored on storage media (e.g.,computer-readable medium). Some of the above-described functions may becomprised in EEPROMs, ASICs, or other combinations of digital circuitryfor digital signal processing, connecting and operating with theadaptive processor. The instructions and/or data may be retrieved andexecuted by the adaptive processor. Some examples of storage media arememory devices, tapes, disks, and the like. The instructions areoperational when executed by the adaptive processor to direct theadaptive processor to operate in accord with the invention; and the datais used when it forms part of any instruction or result therefrom.

The terms “computer-readable storage medium” and “computer-readablestorage media” as used herein refer to any medium or media thatparticipate in providing instructions to a CPU for execution. Such mediacan take many forms, including, but not limited to, non-volatile (alsoknown as ‘static’ or ‘long-term’) media, volatile media and transmissionmedia. Non-volatile media include, for example, one or more optical ormagnetic disks, such as a fixed disk, or a hard drive. Volatile mediainclude dynamic memory, such as system RAM or transmission or bus‘buffers’. Common forms of computer-readable media include, for example,a floppy disk, a flexible disk, a hard disk, magnetic tape, any othermagnetic medium, a CD-ROM disk, digital video disk (DVD), any otheroptical medium, any other physical medium with patterns of marks orholes.

Memory, as used herein when referencing to computers, is the functionalhardware that for the period of use retains a specific structure whichcan be and is used by the computer to represent the coding, whether dataor instruction, which the computer uses to perform its function. Memorythus can be volatile or static, and be any of a RAM, a PROM, an EPROM,an EEPROM, a FLASH-EPROM, any other memory chip or cartridge, a carrierwave, or any other medium from which a computer can read data,instructions, or both.

I/O, or ‘input/output’, is any means whereby the computer can exchangeinformation with the world external to the computer. This can include awired, wireless, acoustic, infrared, or other communications link(including specifically voice or data telephony); a keyboard, tablet,camera, video input, audio input, pen, or other sensor; and a display(2D or 3D, plasma, LED, CRT, tactile, or audio). That which allowsanother device, or a human, to interact with and exchange data with, orcontrol and command, a computer, is an I/O device, without which anycomputer (or human) is essentially in a solipsistic state.

While this invention has been described in reference to illustrativeaspects of the invention, this description is not to be construed in alimiting sense. Various modifications and combinations of theillustrative aspects as well as other aspects of the invention will beapparent to those skilled in the art upon referencing this disclosure.It is therefore intended this disclosure encompass any suchmodifications or aspects.

The scope of this invention includes any combination of the elementsfrom different aspects disclosed in this specification, and is notlimited to the specifics of any of the aspects mentioned above.Individual user configurations and aspects of this invention may containall, or less than all, of the elements disclosed in the specificationaccording to the needs and desires of that user. The claims statedherein should be read as including those elements which are notnecessary to the invention yet are in the prior art and are necessary tothe overall function of that particular claim, and should be read asincluding, to the maximum extent permissible by law, known functionalequivalents to the elements disclosed in the specification, even thoughthose functional equivalents are not exhaustively detailed herein.

Although the present invention has been described chiefly in terms ofthe specific aspects of the invention, it is to be understood that thedisclosure is not to be interpreted as limiting. Various alterations andmodifications will no doubt become apparent to those skilled in the artafter having read the above disclosure. Such modifications may involveother features which are already known in the design, manufacture anduse of wireless electromagnetic communications networks, systems andMIMO networks and systems therefore, and which may be used instead of orin addition to features already described herein. The algorithms andequations herein are not limiting but instructive of aspects of theinvention, and variations which are readily derived through programmingor mathematical transformations which are standard or known to theappropriate art are not excluded by omission. Accordingly, it isintended that the appended claims are interpreted as covering allalterations and modifications as fall within the true spirit and scopeof the invention in light of the prior art.

Additionally, although claims have been formulated in this applicationto particular combinations of elements, it should be understood that thescope of the disclosure of the present application also includes anysingle novel element or any novel combination of elements disclosedherein, either explicitly or implicitly, whether or not it relates tothe same invention as presently claimed in any claim and whether or notit mitigates any or all of the same technical problems as does thepresent invention. The applicants hereby give notice that new claims maybe formulated to such features and/or combinations of such featuresduring the prosecution of the present application or of any furtherapplication derived therefrom.

The invention claimed is:
 1. A method, comprising: channelizing areceived navigation signal into a plurality of subband signals, eachsubband signal comprising a plurality of frequency channels; for eachsubband signal, computing linear combiner weights for the plurality offrequency channels based on one or more exploitable symbol streamproperties of the received navigation signal; using the linear combinerweights to combine the frequency channels and excise interference in theeach subband signal, thereby increasing signal-to-noise-and-interferenceof the each subband signal; and combining the plurality of subbandsignals to produce at least one of a detection statistic and ageo-observable estimate of the received navigation signal.
 2. The methodof claim 1, wherein channelizing employs an analog-to-digital converter(ADC) configured to perform symbol-rate synchronous reception andchannelization of the received navigation signal.
 3. The method of claim1, wherein channelizing employs an analog-to-digital converter samplingrate that is equal to an integer multiple of the navigation signal'sbaseband symbol rate.
 4. The method of claim 1, wherein channelizingemploys an analog-to-digital converter sampling rate that is less thanthe received navigation signal's bandwidth.
 5. The method of claim 1,wherein channelizing employs a fast Fourier transform (FFT), and FFToutput bins are employed as the plurality of frequency channels.
 6. Themethod of claim 1, wherein an interference-excising linear algebraiccombiner is configured to perform at least one of using the linearcombiner weights to combine the frequency channels and combining theplurality of subband signals.
 7. The method of claim 1, whereinchannelizing comprises varying the plurality of frequency channels inorder to vary a number of processing degrees of freedom in the eachsubband signal.
 8. The method of claim 1, wherein the plurality offrequency channels is selected to be equal to or greater than a numberof interferers in the each subband signal.
 9. The method of claim 1,wherein the one or more exploitable symbol stream properties comprisesat least one of a periodic signal, known content in the symbol stream, aknown pilot, a known modulation property, and a constant-modulusstructure.
 10. The method of claim 1, wherein the plurality of subbandsignals are contiguous or separated in frequency, and the plurality offrequency channels in the each subband signal are contiguous orseparated in frequency.
 11. The method of claim 1, further comprisingusing known positions of transmitters that transmit the at least onenavigation signal in order to determine at least one of clock rateoffset and ephemeris of a receiver that performs the method.
 12. Themethod of claim 1, further comprising estimating geo-observables fromthe interference, and geolocating one or more sources of theinterference from the geo-observables.
 13. The method of claim 1,further comprising communicatively coupling to a data service or atleast one navigation signal receiver for receiving third-party basebandsymbol data or navigation data.
 14. The method of claim 1, furthercomprising computing positioning, navigation, and timing (PNT) analyticsusing the at least one geo-observable estimate, wherein the PNTanalytics comprises at least one of blind Resilient PNT (RPNT)analytics, non-blind RPNT analytics, pilot-exploiting RPNT, ratesynchronization, geolocation, navigation signal geo-observableestimates, navigation signal quality estimates, accuracy of thegeo-observable estimates, and accuracy of the navigation signal qualityestimates.
 15. The method of claim 14, wherein the computing performsanalytics over integration times that are longer than a single basebandsymbol, navigation symbol, or pilot period.